Landlord security responsibilities?

I rented my apartment without signing a lease, but did pay a security deposit. Since I moved in the lock on the outside door has been broken, thus completely compromising the security of the premisis. I have requested to have it fixed for several months, and the landlord claims he will, but i have yet to see it done. My question is, in Schoharie County in the State of New York, is he legally responsible for making this repair? If so, whom should I turn to in order to make this happen? Thank you for your help.

Most states have a variant of the "repair and deduct" theory, which allows a tenant to deduct from his rent an amount equal to one month rent to fix a problem that breaches the warrant of habitability that the landlord has had fair notice of and failed to fix.
What you do is send a letter to the landlord summarizing the problem and stating your intention to take care of the problem, since he has failed to do so. You then take care of the problem, buy a good sturdy lock at any hardware store and replace the broken one. Keep without fail all receipts.
Since the landlord makes a warranr of habitability when he rents you the unit, and one thing that breaches that warranty is an unsecure front door, yes he has a duty to take care of the repair. If you follow the above procedure you should be fine.

the renter should be made to be safe and secure by all means available by the landlord, renter of unit at the time that the renter is in occupation of the unit, apt,home,etc. No matter what county, state in the U.S. you must feel secure in the home of what you are dwelling in as long as rent as being paid or the general upkeep and security of the home. If you are responsible for the damage than you will be charged accordingly. There is no reason why the maintenance guy did not repair the lock/ give you a key unless you are not on the lease. if you are not a signed lease holder, you will never be let in at decent properties. I wish you the best of luck!