Most adoptions are filed in the Probate and Family Court of the county where the adoptive parents live. See Where Do I File for a list of courts.  

Sometimes adoptions are filed in Juvenile Court or in District Court.  Adoptions are filed in Juvenile Court only when they have a pending case involving that child, usually  through a care and protection that moves to a termination of rights case. Gloucester and Brookline District Courts retained their jurisdiction over juvenile matters, but they are exceptions to the general rule.