When Bernard Avery Redman was shot and killed in mid-August, few in the Indian Head Manor Apartments where the 15-year-old youth lived wanted to talk about it. And no one could identify those responsible for firing that fatal shot.

Despite dozens of man-hours and countless interviews, Prince George's County police homicide detectives "were at a dead end," recalled Officer Carol Landrum. "They had talked to all the witnesses and had gleaned all the information they could" and still had no suspects.

But then, an anonymous woman heard about the shooting on a local Crime Solvers television broadcast and later phoned police with crucial information about the owner of a car seen at the time of the shooting.

The tip led to arrest of two men on Sept. 22 and a third on Sept. 28. All three have been charged with first-degree murder in connection with the death of Redman.

The Crime Solvers program is part of a nationwide effort designed to give the public an opportunity to help police with much-needed information while maintaining complete anonymity. Tipsters are paid $100 to $1,000 in cash based on the importance of the tip to the case. It is funded by businesses and civic clubs.

Although the program often does not command high visibility, Maryland police officers said Crime Solvers is vital to their work.

The Prince George's County program began eight years ago and, according to Landrum, has helped solve 23 murder cases that otherwise would not have been closed because investigators had exhausted all leads.

"We'll take any kind of assistance," said Maj. James Ross, who heads the county's Criminal Investigations Division. "Crime Solvers has been instrumentally helpful in solving a number of cases that we were having difficulty with. If it wasn't for the program, we wouldn't have solved so many. It's a very good program."

Since its beginning, the program has resulted in the arrest of 484 people and the recovery of almost $700,000 worth of stolen property, and closed 24 attempted murder cases, 11 rape cases, 124 armed robberies and 104 burglaries.

Officer George Ludington, who helped start Montgomery County's Crime Solvers program in 1978 said the program gives the community a chance to get involved with fighting crime.

"You have many, many people who say, 'I want to do something.' Well, here is something they can do," Ludington said. "Without their support, we couldn't have it. This way, they feel they are able to contribute."

Ludington counts more than 989 felony cases closed with the help of the Montgomery County program. Of that, 14 were murder and attempted murder; 61 were robberies; and 8 were rapes. About $1.5 million was recovered in stolen propertyin a decade.

Similar programs designed to curb crime are in place in Charles County and in Northern Virginia. In Baltimore, Metro Crime Alert begins payments at $1,000 and has helped solved dozens of homicides and drug cases in Howard, Anne Arundel and Baltimore counties and Baltimore City.

"We've gotten some very outstanding cases . . . in here," said Officer Nelson McKenna.

The program may have been at its best in a highly publicized case last month when Dennis Derner called the hot line. The D.C. firefighter had just returned from a routine fire call in a run-down Anacostia apartment complex where he noticed two women with a baby whom he believed to be Jeremiah Thate, who had been abducted from a Prince George's hospital when he was three weeks old.

He called Crime Solvers and the county's homicide unit. The next week, an anonymous person called the program with a tip that matched Derner's. Within days, the Thates had their baby back.

Last week, Derner was honored at a Crime Solvers dinner in Prince George's and presented with his share of a $16,600 reward.

"After many, many calls, we finally got the call we were waiting for," Landrum said during the dinner. "Mr. Derner is an unusual person because he refused anonymity."

Despite the recent publicity, Ludington said there are some tough cases with which the police need help. During a recent broadcast, he asked for help in a robbery case that has been troubling detectives since November 1985 when it became a biannual event.

Each spring and fall, a man slips on a black motorcycle helmet, pulls down the shield covering his face and goes to a bank -- with a gun. And he always has left with a sack full of cash. In fact, Ludington reported, the robber has twice robbed the same bank.

"He's good," Ludington said. "His disguise is working and his method is working."

The Crime Solvers telephones are answered 24 hours a day. Here's whom to call when you have a crime tip:

Prince George's County, 735-1111; Montgomery County, 840-2444; Calvert County, 932-6909; Charles County, 535-1470; Metro Crime Alert, 301-276-8888.