David Montenegro, whose request was rejected by the DMV in 2010, asked the state Supreme Court to rule, according to CBS Boston.
Department of Motor Vehicle regulations say a vanity plate can be denied if a reasonable person might find it offensive to good taste.
"It was an accusation against all officers relative to their morality and their position as law enforcement officers," said state Associate Attorney General Richard Head, who argued on behalf of the DMV in Wednesday's (Thursday's) court hearing.
Montenegro, an accountant who represented himself at the hearing, claims his free speech rights are being violated.
"If I could condense all of the problems that I've seen in New Hampshire government down to a single sound bite small enough to fit on a license plate, 'COPSLIE' would be it," he said, after the hearing.
He told CBS Boston says he has been arrested twice for attempted jaywalking and protesting police misconduct.
The New Hampshire Civil Liberties Union joined the case on his behalf and calls the DMV's regulations too broad and discriminatory.
"I think what this case is addressing is a regulation that vests a tremendous amount of discretion in people who sit behind a desk," said Gilles Bissonnette, staff attorney for the NHCLU.
"The decision as to whether it's offensive to good taste is inherently subjective and depends on who's making the evaluation," said Associate Justice Carol Ann Conboy.
Justices will likely take several months to reach a decision on the COPSLIE plate.
Oh, and by the way, the plaintiff, David Montenegro, has changed his name to "human."