According to the Maryland State Police, Eddie -- best known for playing nerdy Eugene Felsnic in the original 'Grease' movies -- pushed his way inside a privately-owned nursing facility on April 8 and refused to leave after a woman inside told him to scram.

Cops say the woman told them Eddie almost forced his way into one of the rooms before getting the boot, but she says he refused to leave the property and got busted when officers showed up.

Police say Eddie was at the place earlier in the day and was told skedaddle ... but Eddie came back that night and that's when police were called. The alleged victim told cops ... Eddie's been by her place several times before, claiming he usually leaves behind items with accompanying notes.

A neighbor who lives a few doors down from where Eddie was busted claims his security camera shows him approaching his property as well that night. He said he was watching TV with his fiancé when he heard something outside and saw Eddie on video trying to open the front door, so he called the cops.

Cops say Eddie's charged with fourth-degree burglary, two counts of trespassing and one count of disturbing the peace.

Eddie was involved in a bizarre situation last year ... when a Maryland waitress accused him of being a creep and harassing her ...  Deezen went on social media and accused her of cyberbullying.

Eddie was also arrested last year at a Maryland restaurant, with cops saying he refused to leave after causing a scene and chucked plates at police during the incident.

People who say they're close to Eddie shared an update on Facebook, claiming he's battling issues and his family is doing all they can to help him.