What was their first clue?

we’ll need a second opinion

Death of NYC man found with sheet wrapped around head ruled a homicide

Nothing gets past New York’s Finest, not even subterfuges and red herrings.

“Yeah, there were some bolsters over his head, too”, Officer Joe Bolton told FWIW, “so at first, we thought it might have been some sort of self-love pillow talk gone wrong, but Rin Tin Tin stamped his front paws three times, which is his signal to think again, so that’s what we did.”