Upon the filing of a petition for the adoption of the council-manager plan of government, or upon resolution of the council to that effect, the mayor, only after the petition has been found to be valid, by proclamation issued within ten days after the filing of the petition or the resolution with the clerk, shall cause the question to be submitted at a special election to be held at a time specified in the proclamation, which shall be as soon as possible after the sufficiency of the petition has been determined or after the said resolution of the council has been enacted, but in no event shall said special election be held during the ninety day period immediately preceding any regular municipal election therein. All acts necessary to hold this election, including legal notice, jurisdiction and canvassing of returns, shall be conducted in accordance with existing law.