Under the Local Government Act of 2000, districts must hold a mayoral referendum if a petition is received containing the signatures of at least 5% of the areas electorate.
The number which would trigger such a vote for the Selby District would be 3,179 electors.
There are 11 directly elected mayors in office across the country, most notably in cities such as London where Boris Johnson was elected as their second mayor in 2008.
Other councils which have elected a mayor include the neighbouring borough of Doncaster where the election of 'English Democrat', Peter Davies has proved most controversial.
Davies was elected into office through pledges for the abolition of language translation services for non-English speakers, axing town twinning agreements and slashing over £40,000 from his own salary.
His many opponents however, claim that up to two thirds of the population do not want an elected mayor and passed a vote of no confidence in the mayor earlier this week.
