9:03 AM PT -- TMZ has obtained the police report tied to Justin Timberlake's arrest -- and the cops spell out exactly what they say they saw while Justin was on the road. Per the doc, Sag Harbor police say they first spotted Justin after he blew past a stop sign a little more than half a mile away from the American Hotel ... where he left a get-together with friends.

Cops say that's when they started following Justin ... at which point they claim he failed to stay in a straight line on the road -- tailing him for about another half mile before they finally hit the lights. Justin was eventually pulled over at an intersection -- which is in a residential area, mind you -- and at that point, cops say they suspected he was under the influence.

The signs that cops cite for their determination ... bloodshot/glassy eyes, a strong odor of an alcoholic beverage emanating from his breath, unable to divide attention, slowed speech, unsteady afoot ... and cops go on to say he performed poorly on all field sobriety tests.

One last thing ... cops claim Justin said, "I had one martini and I followed my friends home." There's no mention of Justin's friends intervening in this police report, but we're told friends of his attempted to intervene during this stop ... asking them to cut him a break.

8:44 AM PT -- TMZ has obtained new photos of Justin leaving the police station there in Sag Harbor -- and from the looks of it ... JT is pretty relaxed considering everything he went through.

One photo shows Justin walking by a police cruiser -- and he's rocking a casual 'fit, a ball cap and shades ... and on the face of it, there's no outward distress in his demeanor.

Another photo shows JT and his attorney apparently leaving the courthouse through what looks to be a back garage of some sort. You can see his lawyer holding a briefcase and leading Justin out of the building upon his release.

7:15 AM PT -- Justin was just arraigned and released without bail. He has been charged with 1 count of DWI and cited for running a stop sign and failure to keep in his lane. The next court date is July 26. He's being repped by criminal defense lawyer Ed Burke, Jr.

As for the traffic stop, law enforcement sources tell TMZ cops observed Justin glassy-eyed and they say they smelled alcohol on his breath. They say he failed the field sobriety test when asked to do a one-legged stand and a walk and turn.

6:38 AM PT -- Sources connected to law enforcement tell TMZ, Justin was at the American Hotel partying and almost immediately after he left and began driving, we're told he blew a stop sign. Cops saw that and began to follow him. We're told Justin began swerving and cops pulled him over.

Our sources say cops performed a field sobriety test and asked Justin to take a breathalyzer test, but he refused.

We're also told several of Justin's friends came on scene and tried to convince cops to cut him a break, but they refused. Justin was handcuffed and arrested, and we're told it's all on body cam.

Justin Timberlake got lit up by cops in New York -- and was taken into custody for a DWI ... TMZ has learned.

A rep for the Sag Harbor Police Department tells us the singer is currently in custody at their station ... as SHPD wouldn't disclose more information at this time. But TMZ has confirmed he was arrested for driving while intoxicated.

As of this writing, Justin is still in custody -- although it's routine to post bail, so he should be out soon.

Our sources say Justin went to meet friends at a hotel Monday night in Sag Harbor for dinner -- and around 12:30 AM, we're told he got into his car to drive back to where he was staying ... only to be pulled over almost immediately after he took the wheel.

In any case ... someone connected to Justin tells TMZ it involved some sort of traffic violation, but police tell us they don't take people into custody for garden variety traffic offenses.

Justin is currently on tour with his next show scheduled for Friday and Saturday in Chicago.

We've reached out to his camp for comment ... so far, no word back.