When police detectives can't solve a case, citizens, with a little incentive, sometimes can help--especially if the incentive is $1,000.

Crime Solvers, a police program in the District of Columbia and every area county except Arlington, pays cash for tips on criminals, and in return has solved hundreds of felony cases. The first such program started in 1977 in Albuquerque, N.M., and the first in this area began in 1978 in Montgomery County. Others soon followed.

Each county program has its own "crime of the week" whereby the police request help on a specific crime by appearing on television and giving the information to newspapers. A citizen who phones in a tip that leads to an arrest and indictment is awarded $1,000. Smaller amounts are awarded to people whose tips lead to indictments in other cases.

A caller who phones in with a tip is given an identity number and is told to call back in a few days after the police have had a chance to investigate the tip. The caller is never asked for his or her name.

Montgomery County has spent $45,425 in awards, solved 441 felonies, collected $577,348 in stolen property and recovered drugs valued at $57,699 since its program began. Prince George's County has spent $29,000, solved 203 felonies, collected $147,175 in property and $92,655 in drugs since it started in November 1979.

The reward money comes from private donations, mainly from businesses, collected by a board of directors made up of local citizens.

Every weekday, local crime solvers programs take turns speaking on TV Channel 7's noon newscast about their crime of the week. Then the phone starts ringing.

In Montgomery County, officer George Heinrich fields the calls at 840-2444.

Officer Carol Landrum, coordinator of Prince George's County's program, recently asked viewers to look for Steven Patrick Nagel, a suspect wanted in a Feb. 24 stabbing in Lanham. After Channel 7 broadcast the telephone number, 735-1111, every extension on her office phone lit up and two officers were there to answer the calls.

The first 10 callers hung up without saying anything. The first voice said, "Your mother did it." And then four legitimate calls came through. Three reported seeing the suspect in a certain town in north Prince George's; another said he sees the wanted man sleeping every night near the Pentagon.

During the following week, after the suspect's picture appeared in local newspapers, another 20 calls were received by police, one of which was from an acquaintance of the suspect. The caller said Nagel was living with relatives in Houston. Nagel was arrested and indicted and will be returned to Prince George's County for trial. The caller was awarded $1,000.

A crime solvers tip led to the arrest and indictment of Robert McCormick, 43, of Silver Spring, a teacher accused of sexually assaulting 12 students at a Prince George's County school.

Earlier this year, two suspects were indicted in connection with the slaying of an AKU record store employe during a robbery in January. The case was a crime of the week and a composite photo of the suspects was broadcast and published. Anonymous caller No. 2982 identified the suspects as Kevin Rainsford and Reginald Drake, and they were subsequently arrested, police said.

Major crime in Montgomery and Prince George's has decreased 14 percent in the last year. Prince George's Police Chief John E. McHale Jr. attributes "a large part of that accomplishment to the increased cooperation between the police department and the public in getting involved."