Can I sue my ex-boyfriend for unpaid rent?

Generally, yes. If your names are both on the lease he is equally as liable as you on the full term of the lease. In other words, $645 x 12 = $7740 per year. He is responsible to the landlord for that full amount if you had never paid a dime. You are responsible to the landlord for that full amount if he had never paid. As between you, he is responsible for half or $3720. He paid $2580 and owes you $1140. It is a straightforward matter based on what you state here.

Stop by Parma Municipal Court (Broadview rolls into Parma Muni.) and go to small claims and file a small claims (under $3000) against him as soon as possible. It is easy, you can do it yourself, and it gets resolved relatively quickly.

Now, collecting is a whole other matter. You may get a judgment...but, collecting may be difficult - the court does not make him write out a check. You convert the judgment to a lien and begin collection on the lien.

My favorite with ex-boyfriends is to levy vehicles, seize bank account funds, or garnish wages.

NOW, the most important advice. Just because he owes you, does not mean you do not owe the landlord. The landlord is still entitled to full and complete rent. "My boyfriend moved out" is not a defense to eviction.

This is general advice and informational only - no attorney-client relationship is formed.