Prince George's County police chief John W. Rhoads plans to resign by July 1 and is seeking a medical disability retirement that would give him a pension of $29,700 a year.

Rhoades, 43, cited a recently aggravated back injury when making his retirement request. In addition, a source close to the chief said that after presiding over the department during a traumatic four-year period, Rhoads had "simply had it."

Since Rhoads took over in 1975, the existing tensions between the largely white force and the county's growing black community were intensified by three shooting incidents. During two of these, white officers fatally shot unarmed black suspects.

Then last June, a 15-year-old black youth fatally shot two officers in the Hyattsville police station.

Shortly thereafter, the department's rank-and-rifle officers voted "no confidence" in Rhoads, who had angered many officers by firing one of the policemen involved in an earlier shooting.

"There's no question that John's been in severe pain (from his back injury) recently," said his friend Leonard I. Colodny, "There's also no question he as tired of the hassle."

Last month, almost all of officers openly defied him, staging a one-day walkout to protest the verdict in the case of Terrence Johnson, the black youth who shot and killed two officers

The day before the job action, Rhoads publicly "guaranteed," that his men would be on the job. In a taped message played at roll calls in the police stations, Rhoads pleaded with the men to report to work the next day.

When 143 of 150 officers failed to report the next day, Rhoads was clearly disappointed. That morning he and County Executive Lawrence J. Hogan went to union headquarters to persuade the men to return to work. After making his speech Rhoads slipped on the wet turf behind union headquarters and wrenched his back.

Since then he has appeared for work only sporadically.

If the county medical board, which meets Thursday, agrees with the diagnosis that Rhoads needs either an operation or an extended rest, the chief will receive an annual pension of slightly less than 70 percent of his $47,000 salary.

County Executive Hogan refused to say yesterday whether he had received Rhoad's retirement request. "I refuse to answer that on the grounds that I don't want to answer that," Hogan said.

Hogan added that he hopes Rhoads decides to stay. "I know John has been in a lot of pain lately but I'd like to see him stay. I really hate the idea of losing him."

One of the Rhoads' old opponents, police union president Laney Hester, said yesterday that he has been pleading with the chief to stay. "I don't think people will realize just how successful he's been in doing what he set out to do until several years from now," Hester said.

"I can't think of anyone who could have done what he's done with the department. He is a gentleman. He's really going to be missed."

Rhoads' major achievement in the eyes of major county residents, has been the dramatic drop in brutality complaints against the department since he became chief. In 1974, a year before he took over, there were 114 complaints against against county police officers.

Last year there were 17.

To accomplish this, Rhoads set up strict rules on the use of force by county officers, a move which drew heated criticism from the men. They complained Rhoads was stripping them of the opportunity to protect themselves.

Many men insisted that Rhoads had sacrificed the good will of the men in order to gain the confidence of the community.

"The thing people often forget," Rhoads said recently, "is that I have a responsibility to two groups, the community and my men. Maybe, in trying to balance those two I have let the men down at times."

In recent months Rhoads has worked hard to patch relations with the rank and file, drinking with them at the union lodge, publicly blasting the Johnson verdict after carefully staying in the middle prior to the trial, and praising the men whenever given an opportunity. Those efforts have made him, in the past weeks, as popular as he has ever been during his tenure as chief.

Rhoads grew up in Prince George's County and joined the police force at age 21. Considered liberal by fellow police chiefs he was picked for the job over more experienced officers by former County Executive Winfield M. Kelly Jr. who thought that his ability to work with people made him ideal for such a sensitive position.

Speculation on a replacement yesterday centered on Jack McHale, a retired FBI agent who has been working as a special assistant to Hogan the last five months. Most observers do not think Hogan will decide on a replacement quickly, and most agree that will look outside the department.

Rhoads' decision was forced somewhat by county retirement laws. If he had not retired by July 1 the chief would not have been eligible for the 70 percent disability pension. Instead, his pension would have been limited to 50 percent of his salary.

Friends said yesterday that if an operation or an extended rests helps his back, Rhoads has frequently talked of becoming the chief of a small police department where there would be less strain.

"This means the end of a significant era in this police department," Hester said yesterday, "an era whic, if the next chief handles things right, will be looked upon as the turning point for this department, the point when it turned in the right direction." CAPTION: Picture, JOHN W. RHOADS . . . cites back injury