My tenant did give a verable notice but it states in the lease agreement that written notice be given,it was a month by month can I hold out any money for no written notice

Laws and contracts are designed to keep things clear, not to be devious. Saying it must be in writing is in case there is any confusion or doubt about it, or when it happened, not so that you can withhold money. You had opportunity to tell him or her to put it in writing when you were told, yes? You should refund all monies due. If you want to get technical, demand the notice in writing effective when you receive it, but I think that would be wrong.
As a landlord you of course run into unfriendly situations but you have a vested interest in keeping things calm - your house. You don't want it damaged in revenge because you kept a deposit on a technicality.