No lease signed

I leased from Feb 08 - June 08. The landlord kept saying that i must sign a lease, but they never produced a lease for me to sign.
I then ran into personal problems, and gave them 3 days notice end of June to be out by Saterday 28th June.
They are now refusing to give back my security deposit claiming i never gave them 1 months notice.
I just want to know if they allowed to do this, as we never even discussed notice periods nor signed any lease

What state are you in? If you do not sign a written lease, the state automatically enacts a month to month agreement for you. You need to give the appropriate amount of notice for a m2m in your state. This can be as little as 10 days notice in Alabama, or as much as 60 days notice in Delaware. You must give the state required amount of notice to vacate. Since you gave only 3 days notice, you certainly did not meet the required notice requirements. Most states require 30 days notice. You owe rent for whatever notice period is legal in your state. No doubt your deposit will be applied to this rent you owe. If any deposit money is left after paying for your notice period, and there was no damage to your unit, it should be refunded to you.