Alleged Gilgo Beach Serial Killer Didn't Put Up Fight During Arrest

We now know more about what happened when cops arrested the suspected Gilgo Beach serial killer -- we're told the guy didn't put up much of a fight.

Suffolk County Police Commissioner Rodney Harrison tells TMZ Rex Heuermann was taken into custody without issue .. and despite being suspected of committing heinous crimes, we're told Heuermann remained stoic throughout the process of his arrest.

Here's how it went down, per Harrison -- he says Heuermann was approached by detectives on the streets of NYC Friday ... who then told him he was under arrest. We're told Heuermann asked what for, and they told him it was for his alleged involvement in the Gilgo Beach murders from over a decade ago.

Harrison says Heuermann's response was interesting ... all he apparently said to the arresting officers was "I didn't do that" -- but we're told he did so in a very somber way. We're told he didn't shout or vehemently deny anything ... he just calmly said it wasn't him.

Harrison says they then threw on the bracelets, and that Heuermann didn't resist whatsoever -- he went peacefully and quietly with them. Commissioner Harrison tells us the detectives subsequently read him his Miranda Rights, and that he requested a lawyer.

Some believed his detainment was a bit more dramatic -- especially with footage that's been released showing police trailing him out and about -- however, it was anything but.

As we reported ... NY officials allege Heuermann is responsible for the 2010 deaths of Megan Waterman, Melissa Barthelmey and Amber Costello. Cops also suspect he may have murdered Marueen Brainard-Barnes -- the 4th victim -- but he hasn't been charged for that murder yet.