Tobit is not scripture in Judaism. It circulated widely among Jews, the Qumran copies prove that, and Hebrew and Aramaic versions of the story were still being copied in the Middle Ages, but it never entered the Tanakh, and rabbinic literature does not treat it as authoritative.
It entered Christian use through the Septuagint, the Greek collection the early church inherited and read as its Old Testament, which carried a wider set of books than the Hebrew canon the rabbis settled on. Christian writers cite Tobit freely from the second century onward, chiefly for almsgiving and for the burial of the dead. Jerome, who knew enough Hebrew to know which books stood outside the Hebrew canon, translated it under protest and called it apocryphal; Augustine and the western church went the other way, and it stayed in.
At the Reformation the difference hardened into a dividing line. The reformers held to the Hebrew canon for the Old Testament and moved Tobit, with the other disputed books, into a separate section headed Apocrypha, printed in Luther's Bible and in the King James version of 1611, described as useful reading but not a basis for doctrine, and dropped from most Protestant printings during the nineteenth century. The Council of Trent, in 1546, responded by defining the wider list, Tobit included, as canonical without distinction. The Orthodox churches receive it too, generally under the heading anagignoskomena, the books to be read. The Catholic term deuterocanonical means second in the order of recognition, not second in authority, and Catholics regard it as scripture on the same footing as Genesis.