Deposit and utility costs

If I send a letter to my landlord asking for my deposit back since it has been a month since our contract ended, is it relevant to mention that we have not settled the costs for utilities. I sent him an instant message about it the day after the last day of our contract, and I constantly ask for updates, and I get a weekly response that “it is taking longer than they expected”. Is it my responsibility and I won’t get my deposit back until they handle it?