Suppose the policeman who investigates your apartment burglary slips your valuable watch into his pocket while filling out the burglary report?

What if you believe the fire chief (whose brother-in-law is the town judge) is the person who put the torch to your uninsured house?

Where do you turn if the trusted priest, minister or rabbi counseling you about your religious beliefs and self doubts says you are no damn good and should go to the devil?

Those extreme (one hopes) examples illustrate the dilemma of many, if not most, working women who are sometimes victims of sexual blackmail from bosses. Or from the boss's boss. What do they do? To whom do they complain without being laughed at, ignored or canned?

The subject of sexual harassment is coming out of the closet. And as the stories pour in, the magnitude of the problem becames more apparent.

Several weeks back, IMPACT, an employe-run newsletter within a major federal department (Housing and Urban Development) published results of a limited survey on sexual harassment. Most women said they had been threatened with physical abuse, bad assignments or firing if they didn't play along. Most of the threats came from bosses.

HUD officials said they would investigate the reports -- when they had some! But they pointed out that nobody had ever complained about sexual harassment through official channels. That is remarkable from a department that employs as many men and women as some medium-sized towns have in total population.

Chairman James M. Hanley's (D-N.Y.) House Post Office-Civil Service Committee has assigned investigators to look into the government-wide problem of sexual harassment.

Rosemary Storey, taking complaints for investigators, says her phone (225-4054) is ringing off the hook. She has compiled many horror stories. But officials in agencies where the stories originate say they know nothing of it.

The reason women rarely complain, through channels, is because the complaints often deal with men who outrank them or run the agencies. Sometimes the alleged villains are actually in charge of programs to fight discrimination of this sort.

For instance, complaints have been lodged about two EEO (equal employment opportunity) officers who have allegedly been harassing women they are supposed to help. One report comes from a Treasury Department agency. The agency of the second EEO official wasn't revealed to this column.

One of the EEO officers cited is alleged to have made heavyhanded, unwanted sexual advances to the agency's federal women's program coordinator. She is supposed to work with him on such discrimination complaints.

A Bethesda-based nonprofit organization called New Responses Inc., has been working in government agencies collecting data on sexual harassment. Several hundred people (mostly women) answered questionnaires.

A majority of the women in the survey (64 percent) identified themselves as white; 35 percent were black; 1 percent Hispanic. Most said they were nonprofessionals, or below the management level.

From the profile drawn up by New Responses, most of the men were age 40 to 55, about evenly divided between black and white. Most were present or former supervisors of women who complained about pressure.

Most of the women answering the survey said physical abuse and job threats were common. The same percentage (4 percent) reported they had been threatened with dismissal for noncooperation or had been victims of rape or attempted rape.

Agencies cooperating in the survey were the General Services Adminsitration and HEW units. Many agencies refused to cooperate, although they are now dealing with congressional investigators.

Insiders expect that Patricia R. Harris, HEW's new boss, soon will issue a strong statement on the subject of sexual harassment in her giant department. But strong statements and an understanding woman boss won't do it all. After all, it was HUD that said there had been no official complaints of sexual harassment. And at the time Harris was secretary of HUD.