A one-month investigation by four Prince George's County police officers yesterday resulted in the arrest of a 15-year-old Beltxville youth who is charged with vandalizing the home of a black Beltxville family.

The home of Joeph Miller of 4601 Lincoln Ave. had been vandalized three times since July. Once, the home's electric meter was blown up, and on two occasions the house and car were spray-painted. After the third incident on Nov.9, the officers were addigned to the case.

"For a house to be vandalized once isn't that unusual," detective Stephen Ricker said yesterday. "But when it happens three times you have a problem. And, in acase like this, even thought you can't be sure, it begins to look racialy motivated."

The Millers live in a middle-class spilt-level home on Lincoln Avenue. Ricker said friends and neighbors in the racially-mixed community could see no reason why the Millers had been singled out. "Often what happens is kids see the police come out to a place and they get the idea that they can do it, too," Ricker said. "But usually places are just hit once."

When the Millers' home was vandalized the third time police decided it was time to go beyond routine investigation. Officers Jerome Herskowitz and Norman Miller and detective Charles Stolting and Ricker were assigned to the case.

They began canvassing the neighborhood, staked out the Miller home and began interviewing area teenagers. Finally, on Nov. 17, Stolting was given the names of three possible suspects.

"That was the first break," Ricker said. "Once we had some names we could start asking some hard questions."

In the wake of yesterday's arrest, police still are seeking suspects in the other incidents.

"These things are very hard to get anywhere with, " Ricker said. "There are never any witnesses, never any physical clues and never any evidence. We don't close (solve) many of them."

Statistics bear Ricker out. Last year there were 9.694 incidents of vandalism reported in the county. A total of 827 people were arrested in connection with the incidents.