No, Catholics only worship the Triune God: Father, Son, and Holy Spirit. It would, in fact, be sinful to worship Mary. Theologians call divine worship latria, or the adoration due only to God.
However, in English the word worship is equivocal. In Britain it is often used of high personages, with the meaning of revering or honoring them due to the dignity of their office. David gave such honor to Saul, for example, because God had placed him as king over Israel. Such “worship” is derivative, sourced in the Father, as St. Paul taught (Eph. 3:14-15), analogous to that which the Decalogue commanded for parents (Ex. 12:20; Dt. 5:16).
Unfortunately, the English word “worship” doesn’t convey the subtlety of the Latin used by the Church, and in the United States is reserved for God. The Church’s theological term is dulia, from the Latin word for service. It is the reverence and respect owed to all the faithful servants of God (Mt. 24:21-23), the angels and saints whom God Himself honors with crowns of glory (Prov. 16:31; 1 Tim. 4:8; 1 Pet 5:4; Rev 4:4). We honor them and, in turn, join with them in honoring God, the source of all holiness (Rev. 4:9-11).
Yet, Mary is not just any other saint. She is the Theotokos, the God-bearer, or Mother of God (Luke 1:43; Council of Ephesus, “Against Nestorius”). She is the true Ark of the Covenant who carried the Word Himself, the Bread of Heaven, and the Good Shepherd (Heb. 9:3-5; Rev. 11:19-12:1). The Archangel told her that she was “full of grace” (Luke 1:28), and Elizabeth, moved by the Holy Spirit, called her “blessed among women” (Luke 1:42).
For all these reasons and more, the Church renders to Mary an honor that is greater than is given to all the saints and angels, termed hyperdulia, or the greatest honor. Yet, it is not still that adoration, latria, which we give to God alone, Father, Son and Holy Spirit.