Former President Richard Nixon does not have to reimburse the government for the $50,000 worth of equipment remaining from the security system it installed at his estate in Saddle River, N.J., because it has not increased the value of the property, the government has decided.

The decision was made after Nixon opted at the beginning of last month to drop the Secret Service protection he is allowed as a former president.

Under the 1976 Presidential Protection Assistance Act, former presidents are required to reimburse the government for any improvements the Secret Service might have made on their residence after protection of the house is terminated. Passage of the law followed congressional hearings into the $7 million the government spent on Nixon's old homes in San Clemente, Calif., and Key Biscayne, Fla.

The act calls for the owner of the property at the time Secret Service protection is terminated to "compensate the United States for the original cost of such improvements or other items or for the amount by which they have increased the fair amount value of the property."

Following the removal of some of Nixon's security apparatus, the Secret Service determined that removing the rest of the elaborate security system, including ripping out underground cables and wires, would cost more than leaving it in, a spokesman said. So the service asked the Comptroller General's Office to determine how much the system could be sold for to Nixon.

The answer: nothing.

The reason is that the security system did nothing to increase the value of Nixon's house, which is situated in the rolling meadows of the suburban neighborhood just outside New York, Acting Comptroller General Milton J. Socolar explained in a letter last month to John R. Simpson, the director of the Secret Service. Nixon purchased the 15-room house in 1981 for more than $1 million, and he has made some refurbishments at his own expense.

A review of the house, based on the assistance of an independent appraiser, showed that the "fair-market value of Mr. Nixon's residence has not increased as a result of the security system installed by the Secret Service," Socolar stated. The letter said the appraiser pointed out that the system did not meet the typical demands of the marketplace, although it did not elaborate on what was wrong with the equipment.

"The law only requires the property owner to pay for the retention of the system if the fair-market value of the privately owned property where the system is installed is thereby increased," Socolar added.

John Taylor, an assistant to Nixon in New York, said Nixon's new private bodyguards are conducting an analysis to determine whether the security equipment is still needed. Taylor said Nixon decided to forgo the government protection in order to save taxpayers that cost.

Government officials said Nixon should have nothing to fear, even though his security apparatus does not meet market specifications. Ron King, a General Accounting Office official who toured the house, said the equipment consists of cameras and silent electronic detectors that require personnel to staff a command post in the house's three-bay garage 24 hours a day.

The Secret Service spokesman said, "It's very technical equipment that most people have no use for. If anything, it would probably decrease the value of the house."