PARMA, Ohio -- The on-duty Cleveland police officer who shot and killed a man in Parma on Monday has been identified by sources in the department as Matthew Craska, a 12-year veteran.

What remained unclear Tuesday was whether Craska had authorization to leave Cleveland to investigate what Cleveland police have said was a suspected burglary at the home of an off-duty officer.

Parma Police Capt. Bob DeSimone said late Tuesday that his investigation will focus only on the shooting at Wareham Drive and Pelham Avenue and whether or not it was justified. Whatever happened in Cleveland before the shooting is of no consequence to his investigation, he said.

When that probe is completed, Cleveland's internal affairs unit will review whether Craska obeyed department rules, including whether he had permission to leave his assigned area, Sgt. Sammy Morris said.

Morris said officers are supposed to get permission from a supervisor to leave their area.

The shooting occurred early Monday morning. Craska, 38, drove his cruiser to a house on Wareham Drive, where he questioned Daniel Ficker, according to Cleveland police.

Parma police reported that Ficker became combative. Craska shocked Ficker with a Taser, and when that failed to subdue him, Craska fired one round from his gun, police said.

DeSimone said Tuesday that a knife was found at the scene but he did not think Ficker had it when he was stunned. He added that Ficker was shot in the left side of his chest.

Craska could not be reached for comment Tuesday, and his union president declined to comment.

Craska joined the department in September 1998. Department sources identified the off-duty officer as 40-year-old David Mindek, who joined the force in March 1997.

Mindek suspected Ficker, 27, had taken jewelry, according to family and friends of Ficker's. Court records show Ficker had a felony conviction in 2005 for carrying a concealed weapon and was sentenced to a year of probation. He also had two drug-related convictions and multiple traffic offenses in municipal courts.

This is the second incident in a little over a month in which police from one Cuyahoga County community were involved in a shooting in another city.

On June 3, Warrensville Heights police crossed into Cleveland and shot a man suspected of slashing the throat of his girlfriend's 5-year-old son. Julian Whitaker, 31, is awaiting trial on charges of kidnapping, felonious assault, attempted aggravated murder and aggravated murder. Cleveland police have not released the results of their investigation.

Cleveland police also have not released results of an investigation into the fatal shooting of a gun-wielding felon by off-duty Officer Walt Thomas in April. At the time, Thomas was working a part-time security job at a Cleveland bar without departmental permission -- a violation of policy. He then resigned.

Parma Mayor Dean DePiero, through his spokesman Jack Marschall, declined to comment Tuesday on the shooting but said it's not uncommon for police officers to go into other jurisdictions to investigate a crime.

Craska also was involved in an incident in 2004 in which deadly force was used. But records don't indicate whether force was used by Craska or the officer working with him. Internal-affairs records indicate an investigation into the incident took 524 days to complete and that city prosecutors ultimately determined the use of deadly force was justified.

Records do not indicate whether Mindek has been involved in any uses of deadly force.

A use of deadly force is any action that could cause serious injury, not just shootings. The force doesn't have to result in death.

Craska was involved in at least eight uses of nondeadly force between 2006 and 2011. Mindek was involved in one. Nondeadly force includes all other forms of struggle with a suspect.

Craska also is a co-defendant in a federal civil rights lawsuit filed last fall against the city of Cleveland, Police Chief Michael McGrath and three officers.

The suit, filed by Rafael Correa of Cleveland, contends that the officers used excessive force in arresting Correa in May 2010, near Detroit Avenue and West 28th Street.

Correa had just left a nightclub, and police were responding to a call that an armed man had assaulted someone at the club. Correa says that he complied with police orders but that then-Patrolman James Simone used a Taser to shock him while he was on his knees, according to the suit. Craska and Patrolman Joseph Wright then tackled Correa to the ground and placed him in handcuffs, the suit states.

The city, in a response to the suit, acknowledged that Correa was on his knees when shocked but maintained that he would not follow commands to lie on the ground.

Mayor Frank Jackson honored Craska in 2006 for his Army service in Iraq, according to police correspondence. Mindek was given a special commendation in 2009 for unspecified reasons.

Plain Dealer reporters Amanda Garrett and Henry J. Gomez contributed to this story.