The New York Times reports the headstone included Trump's birth year, 1946, and the epitaph "Made America Hate Again." It mysteriously appeared in the park on March 27 before being taken away by parks department workers.
Police tracked the stone to a monument dealer who gave them the customer's name and security camera footage showing him loading it into a truck.
The Times said police have identified the man as Brian Whitely. He hasn't responded to requests for comment from The Associated Press.
In a March 30 interview with the then unnamed artist, he told the Times he was trying to remind the Republican presidential front-runner "what kind of legacy he was leaving behind."
There is no word who erected the tombstone.