State law allows a city or village to apply in writing to the county board of a county levying a tax for public library services to be exempt from the county library tax as long as the municipality's library levy exceeds a certain amount.  See Wis. Stat. sec. 43.64(2)(b).

Every year DPI publishes instructions for calculating whether your municipality is eligible for being exempt from the county library tax.  Here are the instructions for calculating the 2017 exemption:

http://dpi.wi.gov/sites/default/files/imce/pld/pdf/2017CountyExempCalc.pdf