11:44 AM PT -- The photog, Marcus Santos, has filed a criminal assault complaint against Baldwin with the NYPD. The incident is currently under investigation.
Things got physical between Alec Baldwin and a NY Daily News photographer today ... as Alec was leaving a NY courthouse with his fiancee Hilaria Thomas.
According to the NY Daily News, Baldwin had just obtained a marriage license ... when he got into it with one of their staff photographers, Marcus Santos.
Santos told the paper Baldwin was screaming for him and another Daily News photog to back up ... and they obliged. But Baldwin kept coming -- "He comes after me, starts shoving and punching me -- one time, right in the chin."
But sources connected with Alec tell TMZ ... the photographer almost HIT HIM with the camera and while Alec pushed him away ... he did not punch him.
Moments after the altercation, Alec tweeted, "A 'photographer' almost hit me in the face with his camera this morning #allpaparazzishouldbewaterboarded."
During the altercation, the 2nd NY Daily News photog snapped a shot of Alec with his arms extended and Santos falling back.