Taylor Swift‘s alleged stalker just had his first day in court — and prosecutors made a lot of troubling claims about him … including the allegation he’s gone to her pad dozens of times.

David Crowe — the man who was cuffed and hauled away by cops twice in three days after numerous people said he was lurking around Taylor’s NYC home — was arraigned Wednesday on three separate charges … including stalking in the 4th-degree and harassment in the 1st and 2nd-degrees.

We’re told Crowe did not enter a plea during this court appearance — but he was cut loose from custody … with prosecutors requesting supervised release with strict conditions.

A judge granted their request — so Crowe is technically back on the streets — but the judge signed off on a protective order prohibiting him from trying to contact Taylor … and prosecutors ran through some other disturbing details in court.

Law enforcement officials alleged in their complaint that they’d been informed Crowe had been spotted at Taylor’s Tribeca home upwards of 30 times in the past 2 months.

Prosecutors claim that on a number of these drop-ins, Crowe asked to speak to Taylor. That’s apparently why he’s facing the stalking charge … and why the court wants to keep a close eye on him upon release.

Remember … Crowe was cuffed by copsfor swinging by Taylor’s home on Saturday, and again on Monday.