RCW 35.22.280 Specific powers enumerated.Any city of the first class shall have power:
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(19) To provide for the establishment and maintenance of public libraries, and to appropriate, annually, such percent of all moneys collected for fines, penalties, and licenses as shall be prescribed by its charter, for the support of a city library, which shall, under such regulations as shall be prescribed by ordinance, be open for use by the public;
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http://apps.leg.wa.gov/rcw/default.aspx?cite=35.22.280