Must a landlord return a deposit placed on an apartment before the lease was signed if the lease doesn't get executed?

I own a duplex and am renting out a 2nd floor apartment. I had a tenant pay me 1 month rent and a security deposit (in advance) to hold the apartment. On the day the tenant was to move in, I received a call informing me that the person was not going to move in any longer. The lease was not actually signed by the tenant, however I have already received payments for the apartment. I do plan on returning the security deposit, however I don't think I should return the 1st month's rent. Because of the receipt of money, and the verbal agreement to rent the apt. I no longer showed the apartment to other prospective tenants, and now I am out for a month of rent (as it is difficult to get renters in the middle of the month). Is this something I am able to do?

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