I don't think so. The breach has to be material and a simple oral statement is not even within the terms of the lease. Usually, unless it is in writing, oral statements of any kind are not considered part of the contract. Even if this statement were a material breach you would have to prove it in court. You would have to show how you have been adversely affected by the misrepresentation. Indeed, you would have to show that if it were not for the representation that "there is no crime in the area" you would not have rented the apartment. To prove your case you would either have to be sued for breach of the lease or you would have to sue to get your deposit back.
Landlords rarely sue residential tenants for breach of the lease unless you really tic off the landlord. So if you were to pick up and move you probably, and I emphasize probably, wouldn't get sued but don't expect your deposit back.
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