The city or town sergeant of each city or town, or any special constables as the city or town council of the city or town may appoint, annually in the month of April, shall ascertain and make a list of the owners or keepers of dogs in the city or town and return the list to the city or town clerk on or before the last day of May. The sergeant or constables shall receive from the city or town treasury the sum of twenty cents (20¢) for each dog listed, except in the city of Providence, where the special constable shall receive from the city treasurer a sum fixed by the city council of the city for each dog listed. The city or town clerk shall within two (2) weeks thereafter furnish to the city or town sergeant or to each special constable appointed and sworn a list of all dogs licensed for the current year and a list of those not licensed, with the names of the owners or keepers, and shall, except in the cities of Newport and Providence, post the list in at least three (3) public places in the city or town or publish the list in any other manner as the city or town council may direct. This section does not apply to the city of Pawtucket insofar as special provision is made for that city.