The annual tax levy authorized by RCW 27.12.050, 27.12.150, and 27.12.420 shall be imposed throughout the library district, including any city or town annexed thereto. Any city or town annexed to a rural library district, island library district, or intercounty rural library district shall be entitled to levy up to three dollars and sixty cents per thousand dollars of assessed valuation less any regular levy made by such library district in the incorporated area, notwithstanding any other provision of law: PROVIDED, That the limitations upon regular property taxes imposed by chapter 84.55 RCW shall apply.