Nebraska Homestead Exemption. Nebraska Homestead Exemption Application, Form 458.The Cook County Assessor's Office administers property tax exemptions that may contribute to lowering veteran's property tax bill. Applicants must file a Form PTAX-341, Application for Returning Veterans' Homestead Exemption, with the Chief County Assessment Office. This annual exemption reduces the Equalized Assessed Value (EAV) of a disabled veteran's home, likely lowering the total tax bill. Pursuant to the provisions of Article III, Section 10 of the Constitution of. , homestead, veterana, old age exemptions). 3. A"essed. Hold out the boot for drivers to fill from their window while driving by. Open houses are great for departments to host in the spring, summer or fall.