Police are investigating whether the death of a man whose body was found dumped in bushland on the NSW South Coast was a gay hate crime.

A dog walker found 56-year-old Peter Keeley's bound body in bushland in Broulee earlier this month with injuries to his face and head.

A post mortem was "inconclusive", police said in a statement.

Early on Thursday morning, police arrested two 17-year-old boys at their family homes in connection with the death.