What is the length of time one has to return security deposits to a month to month tenant once they have moved out

What state do you live in?

Some states have no set time frame others do. If there is no written agreement you would have a verbal agreement to what ever terms you agreed to. On my rentals, I would give them back from 14 to 30 days, the longer times were if there was seroius damage or damage where I needed to get more professional bids on repairs

I reside in California

Hope this is helpful

Moving Out
The law stipulates that a landlord do a pre-move-out inspection with you, let you fix identified deficiencies and limits what can be withheld. It also says how long the landlord has to return your money and what he must do to justify any withholding.

According to California Civil Code Section 1950.5:

•The landlord must notify you in writing that you have the right to an inspection and must conduct an inspection of the apartment with you. The inspection should be done in the last 2 weeks of tenancy. The landlord must let you fix anything which is wrong and the landlord is limited to taking deductions for unfixed deficiencies, damage which occurred after the inspection, or damage not found at the time of the inspection.
•Your deposit must be returned to you within 21 days after you move out. Your landlord must give you a written, itemized statement of the reason for any amount withheld from your deposit. Money can be withheld only for:
–Unpaid Rent (talk to a counselor if you are breaking a lease or giving less than 30 days' notice).
–Damage caused by you beyond normal wear and tear.
–“Reasonable” cleaning charges.
•If your security deposit is not returned or accounted for within 21 days, you can sue the landlord in Small Claims (limit is $7,500; if higher, then lawsuit would be in Superior Court Limited Jurisdiction) court for the amount of the deposit, plus twice the amount of the deposit if you can show bad faith, plus any actual damages.

Landlords must provide receipts documenting the costs of claimed repairs or estimates, unless the landlord does the work themselves (in which case they must describe the work done. In either case, if materials are purchased, copies of the purchase receipts must be provided (or estimates).

Protecting Your Deposit When Moving Out
As when moving in, you can take some basic precautions when you move out.
•Be sure to give at least 30 days written notice before you move out. Technically, you are responsible to pay rent for these 30 days and your landlord can deduct “unpaid rent” from your deposit. If you need to move quickly because of conditions in your apartment or if you are breaking a lease, talk to one of the Tenants Union counselors.
•On the day you move out, have the landlord or manager do a final inspection of the apartment with you. Try to arrange an exchange of your keys for your security deposit. Or have the landlord/manager sign and date a statement that the place is clean and in good condition. If the landlord won't exchange keys or sign a statement, take pictures/videos of the condition of the apartment (hold up a copy of the day's newspaper to show the pictures weren't taken earlier).

Stubborn Landlords
If your landlord does not return your money on time or if he unjustly withholds some of it, be prepared to assert your rights. Remember, many landlords withhold all security deposits knowing that many tenants will not take the steps to get back their money.
Go To Small Claims Court...
•Send a letter to your landlord requesting the money. Refer to the Security Deposit Laws (CCC Sec. 1950.5 and SF Admin. Code Ch. 49). Give the landlord a deadline date of when you expect the money.
•If the landlord doesn't respond within a reasonable time, you can take him/her to Small Claims Court. For a small filing fee, you can sue for up to $7,500. In addition to the disputed money, you can sue for statutory damages for your landlord's illegally withholding your deposit. Small Claims Court is informal and no lawyers are allowed. A few weeks after you file a claim, a hearing will be held. You will tell your side of the story and the landlord will tell his/her side. Your written documentation (receipts, inspection report, photos, etc.) will help your case. You must sue in the city where the rental was—if you rented in San Francisco then you must sue in San Francisco.

Security Deposits (http://www.sftu.org/deposit.html)

Whether you are month to month or on an annual lease has no bearing. As noted in the statute that Nohelp posted, the landlord has 21 days to return the deposit or an accounting of how it was used.