?What about the doctor who killed the babies 9 months old?? the man asked. ?That?s murder.? After a few uneasy moments, the man walked out, muttering, ?This isn?t America.?

Mr. Gosar, a Republican, appeared unfazed, but one month after Representative Gabrielle Giffords was shot in the head at a political event in Tucson, members of Congress are wrestling with one of the most fundamental aspects of American democracy: deciding how and when to interact with constituents.

Nearly all the members of Congress who have resumed meeting with the public since the shooting now do so with a police presence ? in some cases a substantial one.

The result has been a growing formalization of an exchange that has long been a hallmark of popular politics, from the raucous town-hall-style meetings during the health care debate to gentler interactions with individual constituents on a Saturday afternoon.

The Capitol Police have directed members of Congress to coordinate their public appearances with local law enforcement officials, something many are reluctant to do because they do not want to introduce new barriers to what are already limited public interactions.

Representative Loretta Sanchez, Democrat of California, said she had been told by the local police during planning for a coming parade in her Orange County district that instead of walking the route, as she has done for years, she would be required to ride inside a vehicle. A police SWAT team would also be dispatched for security, she was told.

?I hope all of this doesn?t keep people from meeting with their constituents,? said Ms. Sanchez, who added that she would walk the route despite the police warnings. ?We have to be accessible.?

Ms. Giffords, Democrat of Arizona, was meeting constituents outside a Tucson supermarket at a ?Congress on Your Corner? event last month when a gunman shot 19 people, killing 6 and wounding 13. Jared L. Loughner, 22, was arrested and charged in the attack. Ms. Giffords is recovering at a Houston rehabilitation center.

Representative Steve Southerland, a first-term Florida Republican, said that at a recent town-hall-style event, the local police put uniformed officers at the front of the room and undercover officers sat among audience members. Mr. Southerland said he thought the augmented security was a reasonable trade-off.

?I?ve got to have contact with people,? he said. ?I look in their faces and see their hope, and I touch their hands and I hug them around the shoulders, and that?s important. If I had to sit behind a computer answering e-mails or responding to letters from constituents, I wouldn?t be doing this job.?

Elsewhere, however, public appearances by members of Congress have been canceled in recent weeks because businesses have expressed concerns about the safety of their employees.

In Colorado, Representative Ed Perlmutter, a Democrat, recently postponed one of his ?Government in the Grocery? sessions because of security worries raised by supermarkets. Mr. Perlmutter, whose office said he had held 70 similar meetings over the past four years, had another grocery event scheduled for Saturday.

?Our preference is to do it in grocery stores, where people are going to be anyway,? said Leslie Oliver, a spokeswoman for Mr. Perlmutter. ?Sometimes people are there buying their gallon of milk and see him and say, ?Hey, that reminds me, I want to ask him about this.? ?

Representative Steve Israel, Democrat of New York, has begun to hold his ?Congress on Your Corner? events at local fire stations instead of more open spaces to make people feel safer.

Other members of Congress say the Giffords shooting has forced them to consider closing local offices in high-crime neighborhoods because of security concerns.

District offices, which are typically storefronts, are a world away from the layers of security that surround lawmakers and their staffs in Washington.

In some cities, local police officers have been advising Congressional staffs to erect barriers and install cameras and metal detectors at their offices.

Carli Brousseau contributed reporting from Scottsdale, Ariz.