Carmelo Anthony -- Police Escort Against Policy ... NYPD Says

Carmelo Anthony just bragged about getting a police escort through the streets of New York City -- there's just one problem ... the NYPD tells us it's against PD policy to give police escorts to celebrities for no good reason.

The NY Knicks star just posted footage shot from inside of a car ... which is following a police vehicle that is driving against traffic on the opposite side of the street with sirens and lights blaring.

You can hear Anthony saying, "Ain't nothing like a police escort in all this traffic."

We spoke with a NYPD spokesperson who tells us ... "As a policy, we do not give police escorts through traffic for celebrities."

It's possible Carmelo's car was following the cop car without the officer's awareness or approval -- but it seems unlikely since Melo's car was driving against traffic on the opposite side of the street.

The NYPD spokesperson added ... "it's difficult to tell if that's an NYPD vehicle. It could be MTA, Port Authority, or any other law enforcement agency in the city."