TALLAHASSEE, Fla. (AP) _ Smokers will have to snuff out cigarettes in stores, hospitals, courtrooms and some offices and restaurants when Florida's Clean Indoor Air Act takes effect Tuesday.

Although the law bans smoking in all indoor public spaces, supporters acknowledge it is so flexible that it is weaker than the many city ordinances it replaced. And there may be no one in charge of enforcing the law, passed by the 1985 Legislature.

''This will help people quit smoking, help non-smokers and make Florida a more pleasant place,'' said Robert Rawls, northeastern director of the Florida branch of the American Lung Association in Jacksonville.

The law prohibits all smoking in areas including government buildings, elevators, jury rooms and doctors' offices. But it allows employers to develop and post a smoking policy that ''takes into consideration'' employees' habits.

For example, restaurants may choose not to designate smoking sections at all if they post a sign telling customers of that decision or they may assign seating according to customer demand.

''We can cover it the same way we handle requests for special seating of any kind,'' said Lois Kostroski, executive director of the Florida Restaurant Association. ''I think this is the most flexible law that exists right now among those in the United States.''

Reaction to the law by businesses is varied, according to a survey by The Miami Herald.

Some businesses, such as Piper Aircraft in Vero Beach, have no intention of banning smoking. Safety manager Garland Hayes said about 85 percent of the 1,650 employees there smoke.

But Miller Industries, a manufacturer of home products in northern Dade County, has taken the opposite stance.

Smokers, who make up only one-fourth of the workforce there, will have to put out their cigarette when a non-smoker walks into the office. Smokers can't light up if they share an office or a company vehicle with a non-smoker.

Both opponents and supporters of the law are confused about how it will be enforced.

Smokers cannot be charged with a criminal violation. They will be fined $100 for the first offense and $500 for each subsequent offense.

''Calling the police won't help,'' said Inspector M.F. Mann of the West Palm Beach Police Department. ''Right now we're more concerned with someone getting shot, robbed, murdered or raped and if someone complains about smoking, we'll get to it.''