If you're a resident of Brockton, just come to the City Clerk's Office at City Hall and give them your name and date of birth. There is a $20 fee (cash or money order only, personal checks are not accepted). If you are out of town, send a letter with your name and date of birth to the City Clerk's Office, 45 School St., Brockton, Mass. 02301 along with the $20 fee (cash or money order only, personal checks are not accepted).
If the birth certificate is for a child you must send a notarized letter with the child's name and date of birth along with a copy of the parent's ID and the $20 fee (cash or money order only, personal checks are not accepted) to the City Clerk's Office, 45 School St., Brockton, Mass. 02301.