I recently got into a verbal argument with my girlfriend and she wanted me to leave the apartment but I refused. She called the police and they came and told me to leave and cool off and address the matter later. They did not arrest me and they said I would not be charged with anything but a police report was made of the incident. Can this affect my green card status or have any affect when I apply for citizenship down the road?
No. The "good moral character" determination is based on convictions and imprisonment for crimes.
If they didn't arrest you, then you should be fine.
You should not have a problem with your application for Naturalization for this.
Don't worry. Without an arrest, detention or pleading guilty to elements of a crime you should be fine.
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.