Does the Catholic Church officially claim that the Bible is insufficient without tradition?

The Catholic Church follows Scripture itself, in claiming that the Word of God is not reduced to the Written Page, but is also from Oral Tradition: 2 Thessalonians 2:15 (New International Version)

"So then, brothers and sisters, stand firm and hold fast to the teachings we passed on to you, whether by word of mouth or by letter."

The CCC says no such thing. The part of the Catechism which covers Sacred Tradition and Sacred Scripture stretch from Paragraphs 74 to 141. While it is perhaps not convenient to transcribe this somewhat large section of the Catechism in this answer, I will select a few paragraphs which speak more directly of Scripture and its relation to Tradition:

75 "Christ the Lord, in whom the entire Revelation of the most high God is summed up, commanded the apostles to preach the Gospel, which had been promised beforehand by the prophets, and which he fulfilled in his own person and promulgated with his own lips. In preaching the Gospel, they were to communicate the gifts of God to all men. This Gospel was to be the source of all saving truth and moral discipline." ^{Dei Verbum 7; cf. Mt 28:19-20; Mk 16:15}

In the apostolic preaching. . .

76 In keeping with the Lord's command, the Gospel was handed on in two ways:

• orally "by the apostles who handed on, by the spoken word of their preaching, by the example they gave, by the institutions they established, what they themselves had received - whether from the lips of Christ, from his way of life and his works, or whether they had learned it at the prompting of the Holy Spirit";^{DV 7}

• in writing "by those apostles and other men associated with the apostles who, under the inspiration of the same Holy Spirit, committed the message of salvation to writing".^{DV 7}

. . . continued in apostolic succession

77 "In order that the full and living Gospel might always be preserved in the Church the apostles left bishops as their successors. They gave them their own position of teaching authority."^{DV 7 # 2; St. Irenaeus, Adv. haeres. 3, 3, 1: PG 7/1, 848; Harvey, 2, 9.} Indeed, "the apostolic preaching, which is expressed in a special way in the inspired books, was to be preserved in a continuous line of succession until the end of time."^{DV 8 # 1}

78 This living transmission, accomplished in the Holy Spirit, is called Tradition, since it is distinct from Sacred Scripture, though closely connected to it. Through Tradition, "the Church, in her doctrine, life and worship, perpetuates and transmits to every generation all that she herself is, all that she believes."^{DV 8 # 1} "The sayings of the holy Fathers are a witness to the life-giving presence of this Tradition, showing how its riches are poured out in the practice and life of the Church, in her belief and her prayer."^{DV 8 # 3}

Therefore, the Church understands Tradition to be the preaching of the Gospel, preached from teacher to disciple, down from the time of the Apostles; and this teaching has, by Divine grace of the Holy Spirit, been kept whole and entire.

One common source. . .

80 "Sacred Tradition and Sacred Scripture, then, are bound closely together, and communicate one with the other. For both of them, flowing out from the same divine well-spring, come together in some fashion to form one thing, and move towards the same goal."40 Each of them makes present and fruitful in the Church the mystery of Christ, who promised to remain with his own "always, to the close of the age".^{Mt 28:20}

. . . two distinct modes of transmission

81 "Sacred Scripture is the speech of God as it is put down in writing under the breath of the Holy Spirit."^{DV 9}

"and [Holy] Tradition transmits in its entirety the Word of God which has been entrusted to the apostles by Christ the Lord and the Holy Spirit. It transmits it to the successors of the apostles so that, enlightened by the Spirit of truth, they may faithfully preserve, expound and spread it abroad by their preaching."^{DV 9}

82 As a result the Church, to whom the transmission and interpretation of Revelation is entrusted, "does not derive her certainty about all revealed truths from the holy Scriptures alone. Both Scripture and Tradition must be accepted and honoured with equal sentiments of devotion and reverence."^{DV 9}

Therefore, both Sacred Scripture and Sacred Tradition transmit the Word of God, and both must be honoured as manifestations of the Gospel that Our Lord preached to his Apostles and, through them, down to us.

134 "All Sacred Scripture is but one book, and that one book is Christ, because all divine Scripture speaks of Christ, and all divine Scripture is fulfilled in Christ" (Hugh of St. Victor, De arca Noe 2, 8: PL 176, 642).

As you can see, a lot of these paragraphs draw themes and quotes from the Dogmatic Constitution Dei Verbum, which was one of the documents published by the Vatican II Council. In it, the understanding of the Conciliar Fathers about Scripture and Tradition are laid out in some detail. I'd like to quote a section, from article 11, regarding Sacred Scripture:

Therefore, since everything asserted by the inspired authors or sacred writers must be held to be asserted by the Holy Spirit, it follows that the books of Scripture must be acknowledged as teaching solidly, faithfully and without error that truth which God wanted put into sacred writings (5) for the sake of salvation. Therefore "all Scripture is divinely inspired and has its use for teaching the truth and refuting error, for reformation of manners and discipline in right living, so that the man who belongs to God may be efficient and equipped for good work of every kind" (2 Tim. 3:16-17, Greek text).

A better question is: Is Tradition also a medium of divinely revealed truth?

If so, then it is on par with Holy Scripture.

First, is the Word of God intrinsically something which is written word?

Scripture itself calls the oral teaching of the Apostles, under inspiration of the Holy Ghost, the Word of God. We know, therefore, that the Word of God cannot be said to be exclusively, or intrinsically, written, at least necessarily:

1 Thessalonians 2:13

Therefore we give thanks to God without ceasing: because that when you had received of us the word of the hearing of God you received it not as the word of men but (as it is indeed) the word of God, who worketh in you that have believed.

So the answer is no, the Word of God can be preached and still remain to be the Word of God (if you took Scripture away after you had preached it, you would have nonetheless preached the Word of God [1 Cor 15:2], proving its written component being accidental, in the 'consequence' or philisophical sense).

The Apostles also conveyed revelation in the form of Tradition: oral, i.e. handed-on, teachings which are to be held to be the truth just as the epistles are held to be truth in the Church.

2 Thessalonians 2:15

Therefore, brethren, stand fast; and hold the traditions which you have learned, whether by word*, or by our epistle.

* spoken word

This further and concretely and explicitly tells us the Word of God is both Scripture and Tradiiton. Since here, Tradition is defined as epistle (written Word of God) and oral Tradition (not a game of telephone—teaching that was simply not written teaching, but which was to nonetheless form the faith of the Church in the same way).

Since oral and written epistle form are two veins of the one term 'Tradition', or, as we might say 'deposit of faith', we cannot only accept one or the other—you'll notice the 'or' here does not have that meaning; it isn't a choice between the oral tradition and the written. We are to hold fast to both. Written Scripture is merely the crystalized Tradition, or Word of God, as oral Tradiiton is.

They would not be distinguished like this if only the written Word is the Word of God.

In Matthew 28:20 we read that Christ taught His disciples to teach everything He had commanded. Yet we read twice in John's Gospel that Christ's actions were not all written down (Jn 21:25). In fact, he uses strong hypberbole to convey this point: all the world could not contain all that could be written of what Jesus said and did.

Asking if removing something will not change anything that will affect your salvation is to question the validity of giving that Tradition in the first place. Did St. Paul suggest tradition, or did he hand it on to be believed just as the rest of his epistles were (1 Cor 11:2)?

Is the light of a fire sufficient enough to constitute a fire? No, it by definition causes the heat. Asking if the the light alone is sufficient is to question the nature of fire. Similarly, questioning the oral and written components of the Word of God is to do the same; namely, question the nature of divine revelation.

As we saw from Scripture, the Word of God, the Tradition or deposit of faith handed on through the Apostles, is both written and oral in nature.

Some Protestants argue that Scripture itself says Scripture alone is sufficient. In reality, any supposed Scriptural evidence neglect or ignore one simple fact: none of the provided texts are actually exclusive.

For one example,

2 Timothy 3:16-17

All scripture, inspired of God, is profitable to teach, to reprove, to correct, to instruct in righteousness, that the man of God may be perfect, furnished to every good work.

Notice what this says: all of the Scripture is inspired. It is helpful for (profitable, helpes toward the end of—) making you able or equiped for ever good work.

It doesn't say only Scripture is inspired. It doesn't say that it exclusively achieves the benefits described.

To make matters worse, it doesn't even include the New Testament, since they didn't exist in its entirety when this was written. It referred to the Tanakh, or Old Testament.

In fact, the same is said to result or be the benefit of purging oneself of bad works (2 Timothy 2:21).

The faith does not only consist in reading the Scriptures, but interpreting them (which itself implies access to an orthodox interpretation of the Church—including and taking into consideration Tradition), applying it (the same applies here), living it.

Yes she (Catholic Church) does. I've copied the pertinent parts from the previous poster's quotes to show this.

82 As a result the Church, to whom the transmission and interpretation of Revelation is entrusted, "does not derive her certainty about all revealed truths from the holy Scriptures alone. Both Scripture and Tradition must be accepted and honoured with equal sentiments of devotion and reverence."

While it may or may not be true that her Tradition sources to apostles, since after all, the Orthodox say the same thing, yet the two groups contradict at a number of well known Tradition points, the whole point in answering your question is for them, Scripture alone as regards all things necessary for salvation, is incomplete. They are quite clear and open about this. Why someone would think otherwise is beyond the scope.

PS From the authentic Catholic mouth 1965:

Consequently it is not from Sacred Scripture alone that the Church draws her certainty about everything which has been revealed.

DOGMATIC CONSTITUTION ON DIVINE REVELATION DEI VERBUM

Can't be any clearer than that.