Alex Hausner, 40, identified as a psychiatric patient, was ordered held Saturday in lieu of $75,000 bail on felony first-degree menacing, and misdemeanor harassment and stalking, the New York Post reported.
Court papers said Hausner -- who has been described as a gay, Jewish white supremacist -- had allegedly been caught by a security camera yelling "I swear to [expletive] God, don't insult me. I'm going to [expletive] you up" at Cooper.
The alleged stalking and harassment began in 2008, court papers said.
Hausner "was told on numerous occasions not to call" Cooper, Assistant District Attorney Rachel Ehrhardt said in court Saturday.
Before his arraignment, Hausner said, "I can prove from my sources that his boyfriend has sent people after me," referencing Cooper's boyfriend, Benjamin Maisani, who owns a gay bar in Manhattan's East Village.
Cooper's lawyer declined comment on the case.