All communications should be done via Certified Mail, Return Receipt Requested. 

A landlord may not demand or receive security, however denominated, in an amount or value in excess of one month's periodic rent.

EXCEPTIONS: A PET DEPOSIT not in excess of one-fourth of one month's periodic rent may be demanded or received when appropriate, but this subsection shall not be applicable to housing agencies organized or existing under the Nebraska Housing Agency Act.  

When you give the landlord a deposit, be sure to get AND keep the receipt EVEN if you give the landlord a check or money order. The amount you give should also be on the lease. Verify the correct is on the lease.

However, some cities may have enacted their own laws with respect to this.

Upon termination of the tenancy, property or money held by the landlord as prepaid rent and security may be applied to the payment of rent and the amount of damages which the landlord has suffered by reason of the tenant's noncompliance with the rental agreement or section 76-1421. 

The balance, if any, and a written itemization shall be delivered or mailed to the tenant within fourteen days after demand and designation of the location where payment may be made or mailed. 

THIS MEANS THE TENANT HAS TO REQUEST THE RETURN OF THE DEPOSIT AND GIVE AN ADDRESS WHERE THE LANDLORD SHOULD SEND IT TO.

If the landlord fails to comply with subsection of the Nebraska Landlord Tenant Act, the tenant may recover the property and money due him or her and reasonable attorney's fees.

The bad faith retention of all or any portion of a rental deposit by a landlord in violation of sections 76-1483 to 76-1488 shall subject the landlord to liquidated damages in an amount not to exceed one and one-half months' rent and reasonable attorney's fees.