TMZ officially submitted a request for a copy of the video -- which we know was taken during the time of the arrest early Tuesday -- and Sag Harbor PD just got back to us with their response ... saying they're denying the request for the footage, and citing a statute that's interesting.

According to SHPD ... the reason they won't drop the body cam video (for now) is because of a specific New York law that deals with the release of public records.

Under the law, one of the reasons for not releasing certain records is when doing so interferes with an ongoing investigation ... and a rep for Sag Harbor PD told us that's exactly why they're not releasing it at this time.

There are other provisions under the statute that give cops an out on releasing this type of stuff -- including the possibility of depriving a person of a right to a fair trial or impartial adjudication -- but cops aren't citing that here.

Remember ... Justin's defense attorney said he was going to vigorously defend his client against the allegations, and that JT would have more to say about this publicly later on.

He also noted they were in the process of obtaining discovery from the D.A.'s office.

It's unclear when exactly Sag Harbor PD's investigation will officially conclude -- or whether they'll actually release the video when it does ... or point to other exceptions under the law.