When a petition is filed, signed by registered voters of a charter city in number equal to not less than fifty percent of the votes cast at the last general municipal election, seeking the adoption by the charter city of the classification of charter code city the legislative body of such city shall direct the county auditor to determine the sufficiency of the petition under the rules set forth in RCW 35A.01.040. If the petition is found to be sufficient, the county auditor shall file with the legislative body a certificate of sufficiency of the petition. Thereupon the legislative body of the charter city shall, by resolution, declare that the inhabitants of such city have decided to adopt the classification of charter code city and to be governed under this title. The legislative body shall cause such resolution to be published at least once in a newspaper of general circulation within the city not later than ten days after the passage of the resolution. Upon the expiration of the ninetieth day from, but excluding the date of first publication of the resolution, if no timely and sufficient referendum petition has been filed, as determined by RCW 35A.29.170, the legislative body shall effect the decision of the inhabitants, as expressed in the petition, by passage of an ordinance adopting for the city the classification of charter code city.