Not sure what type of TT you have but most are made to support a human on top to do maintenance. Get up there and check for old, cracking sealant around every single item that sticks through the roof and any seams. Water will get through the tiniest hole/crack/raised area. Assuming you have a roof AC, check you manual for tightening the bolts that secure it to the roof. You could also remove the inside liner for skylights and fans and check for dampness.
You could have a dealer / service center do a leak test where they do a pressure test to check for leaks.