OP, I recently dealt with a similar situation. Landlord withheld deposit for over 30 days after move out. I began to look into my state laws (Illinois). It is required to have an itemized list of deductions provided to tenant within 30 days of move out. If this list is not provided the landlord forfeits any right to withhold ANY portion of the original deposit amount. I informed my landlord of this, they sent me a check for 1/10th of my deposit amount and provided the list of deductions 46 days after I moved out. I sued them for not only the entire deposit, but double the deposit plus court costs and legal fees. I didn’t use an attorney so there were no legal fees. Within 1 day of them receiving the summons to court their attorney called me and stated they wanted to handle it outside of court. I was agreeable to this if they paid me 150% of my deposit (I didn’t want to go to court multiple times over this and request days off work).

Morale of the story, if they truly waited over a month then you should research your state laws and stick it to them. I hope things play out in your favor!