I am moving out of an apartment with a month to month lease. Landlords are claiming I must give them a copy of a signed lease to where I am moving and then they will only charge me prorated rent for the 30 day period or I must pay the entire months rent in full even after the 30 days and they will only return the rest of the rent for the days if the inspection checks out even though I've already paid a security deposit. What is the law?
There is no law which requires a tenant to provide a soon-to-be ex-landlord a copy of the new lease in order to receive a proper rent refund and/or security deposit refund.
You must pay rent only for the actual days you occupy the leased premises. If you give proper 30-day notice and the last day is any day other than the last day of the month, you need pay only prorated rent for the days you actually occupied the premises. For example - if you gave notice on 5/5/12 with a projected move-out date of 6/5/12 and you actually moved out and returned the keys on 6/5/12, you would owe only 5 days' worth of rent.
Technically, the landlord could serve you with a 3-day pay/quit notice on 6/2/12 demanding the entire month's rent. But if you vacate before the 3-days expires, he would not be able to file an unawful detainer action against you in court though you would still owe prorated rent for the days you occupied the premises.
It's a bit unclear what your goal is.
If you wish to terminate a month to month lease, your only obligation under the law is to serve the landlord with a 30 day written notice of termination. You must then pay rent for the entire 30 day period.
However, if you wish to pay LESS than the 30 days rent and move out earlier, then the landlord could ask you for a copy of the new lease in order to consider an accommodation for your benefit.