Section 2. Proceedings under section one shall be begun if in the superior court, in the county in which is situated the place where the husband and wife last lived together or where the husband or wife or parent of the child is living, and, if begun in a district court, in the court having such place within its judicial district; provided, that such a proceeding for an offense committed within the territorial limits of the Boston, the Worcester, Bristol county or the Springfield juvenile court, as designated by section fifty-seven of chapter two hundred and eighteen, if founded upon the same allegations as a proceeding under sections twenty-four to twenty-seven, inclusive, of chapter one hundred and nineteen, may be brought, heard and disposed of in said juvenile courts. Such a proceeding for an offense committed within the territorial limits prescribed for the criminal jurisdiction of any court other than the courts within the territorial limits of the Boston, the Worcester, Bristol county and the Springfield juvenile courts, if founded upon the same allegations as a proceeding under said sections twenty-four to twenty-seven, inclusive, of chapter one hundred and nineteen, may be heard and disposed of in the juvenile session of the court. Any parent placed on probation in such a proceeding in any of said juvenile courts shall at the request of the justice thereof be supervised by the probation officers of the municipal or district courts located within the territorial limits of that juvenile court.