You might want to call them as I could not find any information about filing for an extension.
Income Tax, City Hall Rm. 105
1315 S. Washington Ave.
Saginaw, MI 48601
Phone: 989-759-1650
Fax: 989-759-1467
Office Hours
8:00 am to 4:00 pm, Monday through Friday
City of Saginaw Michigan - Income Tax