A Prince William County man died Tuesday morning at Potomac Hospital after it took 32 minutes for volunteer rescue personnel to reach his home and the two squads that did arrive did not have anyone trained in the use of special life-support equipment, according to hospital and county records.

A call for help for James Overman, 47, of 15150 Woodsman La., was placed to the county's 911 emergency number at 6:07 a.m., according to fire and rescue records. When the closest rescue squad did not respond to a dispatcher's call, a second squad was called. The sequence repeated itself until six squads were called, two of which responded, both arriving at 6:39 a.m. at Overman's home, according to the records.

Overman, who worked for the Office of Management and Budget, received cardiopulmonary resuscitation at his home but was not treated with advanced life support equipment such as defibrillators and heart monitors until he arrived at Potomac Hospital, about four miles from his home, about 7 a.m., nearly an hour after the 911 call was placed, according to the records.

He failed to respond to the treatment and was pronounced dead at 7:21 a.m., hospital personnel said. An autopsy showed he died of a heart attack.

The incident comes as Prince William -- Northern Virginia's second-largest jurisdiction, with 200,000 people -- is grappling with residents' demands for increased services from a county strapped to pay for them. Its jail is crowded, its roads are clogged, its crime rate is rising and its 911 system -- which malfunctioned for 45 minutes earlier this month -- and its volunteer-dominated fire and rescue system have recently come under scrutiny.

County Executive Robert S. Noe Jr. has designated the county's fire and rescue services a major issue for 1988. Critics of the system have cited concerns such as the fact that paid personnel are not on duty 24 hours a day and that advanced life support is not consistently available.

"This is what I had feared," Noe said yesterday. He said he had asked for a written report on the incident from Selby Jacobs, director of fire and rescue services.

Northern Virginia Medical Examiner James C. Beyer said that although it is impossible to say whether response time played a role in Overman's death, "the general rule of thumb is that the sooner the treatment, the greater the chance for success."

Dr. Thomas Ryan, medical director for Prince William County's western half, declined to comment specifically about the case but noted that the American Heart Association advises that CPR be given within four minutes of cardiac arrest and that ALS be administered within eight minutes. "Any prolongation of those times decreases a patient's chances," he said.

Overman's wife Charlotte asked yesterday about the half hour it took for help to arrive for her husband, responded: "Is that all it took? I thought it was an extraordinary amount of time." Overman, reached in Hinton, Iowa, where she was preparing for her husband's funeral Saturday, declined to comment further.

Prince William is served by 109 paid, nonadministrative fire and rescue personnel and more than 700 volunteers divided among 12 autonomous fire companies.

Paid personnel work from 7 a.m. to 5 p.m. Monday through Friday, leaving what critics have called "windows of vulnerability" at certain times on weekends and on holidays, and during the 5-to-7 morning and evening rush hours. It was during this time -- when critics say the service is additionally vulnerable because volunteers may be commuting to or from work -- that Overman needed help.

"I don't know how to describe this other than it is absolutely deplorable," Supervisor Edwin C. King (D-Dumfries) said yesterday. "And I don't say that to show disrespect to the volunteers. They are just that -- volunteers" who have other responsibilities. "It is very unfortunate and regrettable that he {Overman} had his heart attack at the worst possible time for the system."

"We have known the exposure exists; the supervisors have known," Noe said. "I had hoped we would be able to address this before we had an incident like this to point it out so vividly."

The fire chief for the two rescue stations called first to help Overman did not return a reporter's phone calls yesterday.

Chief Billy Spicer of the Occoquan-Woodbridge-Lorton volunteer company, which had secondary responsibility and which also did not respond to two calls from the dispatcher, said he had not heard of the incident, but "obviously there was a shortage of manpower . . . . "