The old fight over federal aid to church schools broke out in the Senate again yesterday.

Sen. Daniel Patrick Moynihan (D-N.Y.) started it by offering an amendment to a college aid bill, giving grants to students from low income families at private and church-sponsored elementary and secondary schools.

The amendment would permit a maximum grant of $750 a year to help pay tuition for a student from a family with income of not more than $15,000 a year. Moynihan has been trying to get such a bill passed since he came to the Senate four years ago.

Sens. Ernest Hollings (D-S.C.), Henry Bellmon (R-Okla.) and others fought the proposal on grounds it would add at least $160 million to federal spending the first year and more later. They also contented it would be a breach of the constitutional separation between church and state. Bellmon read an opinion from Attorney General Benjamin Civiletti that the proposal is unconstitutional.

The bill would authorize an estimated $36 billion over the next five years to continue programs aiding colleges and students. The bill has been cut in committee well below the $60 billion measure approved by the house, but efforts are expected to try to cut it further.

The big money in the bill is for student grants. The House increased present grant levels by raising both the maximum dollar amount and the percentage of tuition a grant could equal to accommodate public and private colleges. The Senate committee cut the ceilings in both categories.