Nebraska Homestead Exemption. Nebraska Homestead Exemption Application, Form 458.Please call their office at 402-593-2203 to request a letter for the Homestead Exemption. Disabled veterans who own their homes (in fee simple) may be eligible for a property tax exemption. The Nebraska homestead exemption program is a property tax relief program for six categories of homeowners. Three of these categories are specific to Veterans:. Like the homestead exemption, only school districts are required to offer this exemption.