One-month Lease Back Requirements

[Amanda Lodge]

Hi All! 

I'm submitting my very first offer today on a property that will eventually become a rental property. The seller would like to lease back the property for one month after closing, which works out perfectly for me since that's when the lease on my current apartment ends. 

My question is: should I require a security deposit and have them sign a formal lease? I'm not sure how this typically works. 

Thanks!