Overlapping Leases, Am I guaranteed pro-rated rent?

[Snooze]

Hi All,

I've been searching for the answer to my question but haven't found any info for laws within NYC.

We found a great apartment and signed a lease beginning a month before our other lease expired, so we essentially have two apartments for one month.

Here is my question, the girl moving into our old place wanted it early and the realtors said that they would pro-rate our rent if we got out early, but we would have to wait to get the pro-rated amount with our deposit (after we turn over our keys).

First, are there laws guaranteeing me that the Landlord will have to pro-rate my rent if there is someone else under a lease starting before my lease is over? AKA, can the landlord legally have two different tenants under different leases for the same apartment at any given date?

Since we're dealing with one of the less-reputable brokers in Brooklyn (I'm sure you can guess who), we're skeptical. They said they would put something in writing, but I'm not sure it would do any good if the landlord doesn't sign it.

Am I overreacting? Any help is greatly appreciated.

Thanks,
S