The county commissioners shall have the register so prepared as to permit the assessor or registry assessor to insert the party enrollment of each elector. Upon the receipt of the certificate of enrollment from the elector, the assessor or registry assessor shall insert in the register, after said elector's name, his party enrollment: Provided, however, If an elector has at any time received party enrollment under the provisions of this act, it shall be the duty of the assessor or registry assessor to insert in the said registry, from year to year, at the time of making the annual assessment, said party enrollment, after the name of the said elector, until such time as a certificate of enrollment is presented to or filed with him by the said elector to a contrary effect. Each elector, not already enrolled, desiring to participate in the primaries, must file with the assessor or registry assessor his enrollment certificate. If an elector does not desire to vote at a primary election, he shall not be required to sign or execute the above certificate as to his party affiliation or membership, and such party affiliation shall not be recorded.