Lakewood , Washington -LRB- CNN -RRB- -- Whoever fatally shot four police officers Sunday in a coffee shop outside Tacoma , Washington , may have been wounded by one of the victims , police said . Authorities are trying to determine who killed four Lakewood police officers in the shop in neighboring Parkland on Sunday morning . Investigators are checking with area hospitals to determine whether the gunman sought treatment after the shooting , Pierce County sheriff 's spokesman Ed Troyer said . `` There 's ... evidence that a Lakewood officer fired some shots , and we hope he hit him , '' Troyer said . Troyer said authorities are seeking Maurice Clemmons , 37 , of Pierce County as a `` person of interest . '' He did not identify Clemens as a suspect . Authorities identified the victims as Sgt. Mark Renninger , 39 ; Officer Ronald Owens , 37 ; Officer Tina Griswold , 40 ; and Officer Greg Richards , 42 . The officers were sitting in the coffee shop before the start of their shifts when a gunman shot them at about 8 a.m. PT , Troyer said . The shop is a place where area law enforcement officers regularly gather to share information , he said . The attacker walked to the counter as if to order coffee before he pulled a gun out of his coat and fired , Troyer said . Two of the officers were `` executed '' as they sat at a table , another was shot when he stood up , and the fourth was shot after struggling with the gunman all the way out the door , Troyer said . `` After , we believe , some of the officers were shot , one of them managed to fight his way with the suspect ... all the way out the the doorway until he was shot and died of a gunshot wound , '' Troyer said . Sunday 's incident was the first time the Lakewood police department lost any officer to a shooting . Two employees of the coffee shop and other customers inside Forza Coffee Company were unharmed , Troyer said . One employee fled through the back door when she saw the shooter pull out his gun , he said . `` As you can imagine , they are traumatized , '' he said of those inside the coffee shop . `` Some are in shock . '' Investigators have not come up with possible motives , police said . Families of the officers have been notified , Troyer said . All of the officers were in uniform , wearing vests and had marked patrol cars parked outside , he said . Police are looking for one man in connection with the attack , though authorities are not ruling out the possibility that a second person was involved , Troyer said . A $ 10,000 reward was offered for information leading to an arrest , he said . Surveillance tapes from multiple location are being reviewed . Authorities were conducting searches in numerous locations , and dogs had been brought in to attempt to track the shooter , Troyer said . Investigators believe Clemmons , the person of interest , `` is intentionally avoiding us , '' Troyer said . Clemmons has `` extensive violent criminal history from Arkansas , including aggravated robbery and theft , '' the sheriff 's department said in a statement . He also was recently charged in Pierce County in connection with the assault of a police officer and the rape of a child , according to the statement . According to a local prosecutor in Arkansas and past articles published by the Arkansas Democrat-Gazette , a repeat offender named Maurice Clemmons had his 95-year prison sentence commuted in 2001 by then-Arkansas Gov. Mike Huckabee . Huckabee cited Clemmons ' young age -- 17 at the time of his sentencing -- when he announced his decision , according to newspaper articles . `` It was not something I was pleased with at the time , '' Larry Jegley , who prosecuted Clemmons for aggravated robbery and other charges in Pulaski County , Arkansas , told CNN Sunday . `` I would be most distressed if this is the same guy . '' Jegley said he was told Sunday by `` media and police agencies '' that the former Arkansas inmate was the same man being sought in Washington state . Some tips have come in , and investigators were following leads , one of which turned out to be `` an unfortunate hoax , '' Troyer said . A Tacoma man called `` multiple people '' claiming to be the gunman , though authorities determined the man was lying . The man was arrested and now faces obstruction charges , Troyer said . A couple of blocks surrounding the coffee shop were cordoned off . Several other police agencies were on scene to assist . Washington Gov. Christine Gregoire , in a statement , said she was `` shocked and horrified '' at the shootings . `` I offer whatever support is needed to the Pierce County Sheriff in their search for the perpetrator , '' Gregoire said . Lakewood is about 40 miles south of Seattle and 10 miles southwest of Tacoma . See a map of where the shootings took place Bystanders gathered outside the Forza Coffee Company , some of them in tears as they spoke to CNN affiliate KING . The coffee shop is on the edge of McChord Air Force Base . Spokesman Bud McKay said the base was not shut down , but security was ramped up around the perimeter as a precaution . The military has offered assistance to police , he said , but it has not been requested . CNN 's Patrick Oppmann , Samira Simone , Dave Alsup and Dina Majoli contributed to this report .