I believe that if you have not signed a lease you have a month-to-month tenancy and the landlord can start the proper eviction proceedings if that is what they want to do.
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Did they give you the keys and possession of the premises? If so, and you have not signed a lease, then you have a month-to month tenancy which may be canceled at any time upon 30 days written notice. If you have not been given keys and possession and there is a written lease that has to be signed then you don't have a contract until a fully executed lease is returned to you. The landlord could chose to refund the money to you and not execute a lease.
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Without keys, you cannot move in. Without a lease, you may not have a contract.
If you signed a document, also signed by the landlord and or authorized agent, where the apartment you "rented" is described, by address, a rent term is expressed (for example: one year from March 1, 2013 to February 28, 2014), states the monthly (or annual) rent, states date for delivery of possession, then that document may be considered a lease.
If you have a "receipt" only, or if you signed an "application" you may not have a lease.
You may want to visit an attorney.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.