A graduate student who recently had his automobile towed by Ellery Garage in Cambridge said yesterday the towing company tried to over-charge him for storage rates on his car, a possible violation of existing Massachusetts law.

The graduate student, who asked not to be identified, said yesterday Ellery Garage refunded $2 to him only after he contacted an investigator for the Department of Public Utilities. The investigator then called Ellery Garage president Roger Starr and instructed the towing company to refund the money. The investigator, Charles Ivers, confirmed the sequence of events yesterday.

The student also said Ellery Garage originally charged him $6 for storing his car for a period of less than 48 hours which spanned three calendar days.

The student said the towing company should have charged him $4 for storing his car, adding that Ellery Garage had attempted to base the fee on the calendar day period rather than the actual hours during which the automobile was held at the garage premises.

Massachusetts law and a contract between the City of Cambridge and Ellery Garage state that charges imposed for storage of vehicles that are towed away shall not exceed two dollars for any 24-hour period. The statute is part of Chapter 40, section 22d of Massachusetts state law on traffic regulations.

A February 10, 1977 memorandum signed by George Teso, director of the Department of Traffic and Parking for the City of Cambridge, also sets forth the $2 per 24-hour period regulation.

Ellery Garage management said yesterday the towing company charges storage rates according to state law. A management official, who refused to identify himself, also refused to produce a written company policy on storage rates saying the Crimson "was not a customer."

Ivers said yesterday the Department of Public Utilities has received complaints similar to that of the graduate student from motorists whose cars Ellery Garage has towed.

He said some towing company personnel interpret the regulation in terms of calendar days rather than 24-hour periods, adding "This is something that we have to educate them on.