According to the Jewish Encyclopedia entry on Tobit:
The text exists in Greek, Latin, Syriac, and Judæo-Aramaic, besides two late Hebrew translations.
The excellent Greek style of the Sinaitic may suggest a Greek original. In view of the conflicting character of the data, it is best to reserve opinion as to the original language; the text appears to have suffered a number of revisions and misreadings.
But I note that this entry predates the Qumran discoveries. Wikipedia suggests:
The book was possibly originally written in one of the forms of the Aramaic language. Jerome described his version for the Vulgate as being made from an Aramaic text available to him. Four fragmentary texts in Aramaic and one in Hebrew were found at Qumran.
What is the current state of scholarship? Is a Greek original still a viable possibility?