Not long after police arrived to view James A. Cooley`s body and its bashed-in head, the local police chief said suicide was a likely cause of the man`s death on April 6 in Hobart, Ind.

That determination now lies at the heart of an official controversy over whether it is possible for a person to commit suicide by hitting himself on the head 32 times with a claw hammer.

And if so, could it be done without leaving fingerprints on the hammer?

More than six months after the fatal incident, Hobart Police Chief Lawrence Juzwicki and his detectives are convinced that Cooley, 52, a railroad supervisor who had cancer, inflicted 32 hammer blows to his head while alone and despondent in his home at 28 N. Illinois St.

But Dr. Daniel Thomas, the Lake County, Ind., coroner, is convinced the case is one of murder.

He contends that Cooley was ''hit from behind'' and that taking his own life would have been ''humanly impossible.''

Thomas officially has classified the death as a homicide.

''This is a bizarre case,'' said Juzwicki, a college-educated, 12-year police veteran in Hobart, a small town of millworkers near Gary.

He has based his conclusion in part on the opinions of two out-of-state experts and on research that he says shows there are other documented cases of suicide just as bizarre.

But, Thomas asks, who could kill himself by hitting his head with a hammer 32 times? Cooley would have fainted or gone into shock after the first blows, he says.

The weapon, a claw hammer owned by Cooley, was found on the floor next to his left foot. Evidence technicians lifted a partial palm print from the bloody hammer, and authorities agree that it was not Cooley`s.

''Ours is the final decision as to cause of death,'' Thomas said. He has publicly called on the police to reopen their investigation.

Juzwicki has not agreed to do so but has said he would be open to a county grand jury review of the case, which has become a battle of forensic experts from Indianapolis to Oregon.

Both sides point to medical findings and other evidence to support their conclusions.

Hobart police note the absence of any sign of a struggle where Cooley`s wife, Diane, found his body slumped behind a closed door in his makeshift basement photography darkroom.

They say nothing was missing or disturbed in the home, there was no forced entry and there was no indication, such as wounds on his arms and hands, that Cooley had resisted an attack.

Ten of the 32 head wounds were ''very deep,'' according to an autopsy by Dr. Young Kim, a coroner`s pathologist. All the wounds formed a ''parallel''

path stretching almost from ear to ear over the top of the head.

Thomas contends that Cooley, who was right-handed, could not have inflicted the blows to the left side so ''equally.'' He believes there were no other wounds because Cooley was left woozy by the initial blows and, therefore, unable to ward off the attack.

Mrs. Cooley said the locked house was just as she had left it when she went shopping a few hours earlier, but she has told investigators that she does not believe her husband took his own life.

In a public statement issued in support of the suicide theory, Juzwicki disclosed that Mrs. Cooley had passed a lie-detector test in the case and had furnished a detailed account of her activities on the day of her husband`s death.

The palm print on the hammer did not belong to Cooley or his wife or to any of the paramedics, detectives and others who were in the basement on official business after Cooley`s body was found, Thomas said.

But Juzwicki said: ''Our department conducted a lengthy and thorough investigation that involved collection of evidence, interviews, polygraph tests and a review of all of our findings by a forensic pathologist and a blood-spatter expert.''

Dr. Larry Lewman of the Oregon state medical examiner`s office and Sgt. Rod Englert of the Multnoamah County (Ore.) Sheriff`s Department ''both concluded with certainty that this case was a suicide,'' Juzwicki said.

He said he turned to the Oregon specialists on the recommendation of two of his officers who met Englert at a police homicide school last year.