Whether or not the storage unit attached to the apartment that you leased is yours for access depends upon what the written lease states or does not state in that the lease controls the obligations owed to you by the landlord and vice versa in the absence of conflicting state law.If the lease that you signed for the unit you occupy does not state that the storage unit attached to the property is not part of the rental then by the landlord's failure to mention this in the lease that you signed, presumably the storage space comes with the rental.I would first call the landlord about the situation you have regarding the storage unit and follow up with the conversation with a letter memorializing the conversation. Keep a copy of the letter for future use and need.