In a cold spring drizzle, about 1,000 area police officers turned out yesterday to pay last respects to Montgomery County policeman Philip Metz, shot to death last Friday when he surprised a pair of burglars in a catalogue discount store.

A police honor guard holding flags and rifles stood at attention outside St. Catherine Laboure Roman Catholic Church on Viers Mill Road as Metz's parents and county dignitaries filed inside, followed by crowds of officers from 42 different police departments as far away as Delaware and Annapolis.

"How fortunate we are to have known him," friend and fellow officer Jack Carnahan said of Metz, a Boy Scout leader and nine-year veteran of the force. Carnahan's voice trembled as he said, "How proud we are to have been his friends." Members of Shift 5, Metz's unit at his station in Silver Spring, looked on from a front pew.

A woman officer touched a handkerchief to her eyes. Later a police lieutenant sang "Amazing Grace" and "The Battle Hymn of the Republic." The muffled squawk of police radios was heard occasionally.

Metz, 33, was killed inside the New Hampshire Avenue premises of W. Bell & Co. along with security guard David Myers, who was also interred yesterday in separate services. Metz was the first policeman to die in the line of duty in Montgomery County since 1976.

After services were completed, a single-file motorcade of hundreds of police cars, their dome lights flashing in a traditional salute to a fallen policeman, escorted Metz's remains to Gate of Heaven Cemetery on Georgia Avenue.

"It's unique that there's such a comradery among the different jurisdictions," said motorcycle policeman Scott Loomis, as the motorcade inched down a closed-off Viers Mill Road yesterday. "But it's too bad that we have to come together for something like this."

(One ranking area policeman who was not in the motorcade was D.C. Police Chief Burtell Jefferson. He received word at mid-service that President Reagan had been shot and, driving a police cruiser himself, sped back to the District escorted by county motorcycle police.)

Rain fell heavily at the cemetery as two buglers played taps, a firing squad sent off volley after volley and Metz's ashes were interred.

Reared in the New York area, Metz completed an undergraduate degree in medical science before moving to Washington. In 1972 he graduated second in his police academy class and by the time of his death had accumulated seven letters of commendation.

Off duty, he directed a Boy Scout troop and held the rank of captain in the Army reserve. He is remembered as a slightly reclusive bachelor who was in love with his job. According to Sgt. Larry Desmond, who once commanded Metz's shift in Silver Spring, he was "quiet, reserved and a good police officer" who always wore his bulletproof vest.

Police now have 10 investigators working full-time on the case. According to preliminary findings released yesterday, Metz was shot in the head when he accosted a burglar in the building's main office. A second gunman jumped out and shot Myers and store manager Douglas Cummins, who was also present, in the chest.

Cummins was then dragged into the office, beaten with pistols and forced to open the safe. The two men escaped with cash and checks, leaving Cummins handcuffed to a file cabinet. He managed to free himself and notify police.

Police are offering a $20,000 reward for information leading to arrests and indictments in the case.