A regional board of education may establish a finance committee for the regional school district. The finance committee shall provide information to the regional board of education concerning local budget issues of the member towns, and any assistance requested by the regional board of education in the preparation of the proposed budget for the regional school district, pursuant to section 10-51. The local board of education for each member town, or the legislative body of a member town in which there is no local board of education for such member town, shall appoint two representatives to the finance committee.