请教关于租约

去年搬到马里兰州，Mentgomery County，租aprtment complex房，租约今年九月中旬到期。我想租约到期时搬出，今天在出租办公室，一个办事员非常坚决地说，她们需要60天的notice，而我只给了30天，所以一定要付到十月中旬，而且要按month-by-month rate 付。我不明白的是，我并没有违约，但租约里确有一项说 “By entering into this lease agreement, you agree that if you do not send us written notice of your intention not to renew your lease at least 60 days prior to the lease end date, your lease will be automatically extended on a month-to-month basis unless we give you notice at any time prior to the lease end date that the lease will end on the lease end date without a month-to-month extension".那么根据这项，能说明我就必须付租约中止后的一个月房租吗？我怎么越读越觉得在两可之间呢？网上查了landlord-tenant handbook,还是似是而非，好像说她们对也能通但并不明确，我还是觉得没道理多交一个月房租。(http://www.montgomerycountymd.gov/content/dhca/images/PDF/handbook_web.pdf）。 请教各位，这种事如何处理？多谢。