The bathroom sink spews out cloudy water, the kitchen faucet's water smells like bad eggs, and you're ready to head for the nearest laboratory to find out exactly what is coming out of your tap.

It's important to know, however, that not all bad-looking water is harmful. For instance, cloudy water can mean that there's some extra lime present. It doesn't look very good, but "it won't cause any harm," said Harry Ways, Chief of the U.S. Army Corps of Engineers Baltimore-Washington Aqueduct Division, which supplies water to the District.

Important warning signs of potentially harmful contamination include:

*Brown or murky water. This may indicate that some silt, rust or other contaminants are getting through the system and into your faucet.

*Water that foams as it flows from the faucet or when splashed in a glass.

*Smelly or bad-tasting water.

*Any sudden change in taste or appearance.

Laboratory testing is both expensive and time-consuming, but water authorities and many local health departments will test water if there is reason to suspect harmful contamination. This testing, which is done a very limited basis, is usually free to the consumer.

Water testing from an independent laboratory can cost anywhere from about $18 for testing water hardness to several thousand dollars for a dioxin screen. It could take anywhere from a day or two to a month to receive results. Experts offer this advice on selecting a lab:

*Look for laboratories that have EPA certification. Ask what their certification pertains to: some laboratories are certified only to do metals testing of water, searching for contaminants such as arsenic, iron, lead and barium. Others have passed rigid tests for certification of pesticides and herbicides. Certification for dioxin testing is even more stringent.

*Is the laboratory also certified or licensed by the state? Most good labs will be.

*Look for a laboratory that will supply the containers for water sampling. This diminishes the chance of contamination. "Not only should they supply the bottles for sampling, but they should also give detailed information for collection of the samples," said Lewis Harris, biochemist and founder of Harris Laboratories in Lincoln, Neb.

*Ask how long the laboratory has been in business and what types of tests they do most frequently. "It's important to look for firms who have been in business for a number of years and can provide staff, education and laboratory experience," said Grover C. Williams, president elect of the American Council of Independent Laboratories.

*Look for a laboratory nearby. Volatile organic chemicals sometimes are destroyed during transport, making it more difficult to get an accurate count.

*If you must send samples to an out-of-town laboratory, make sure that they are shipped overnight and are kept cold during transport.

*Be sure the laboratory will interpret the results.

Two organizations that provide listings of laboratories specializing in water testing are:

*The American Council of Independent Laboratories Inc., 1725 K St. NW, Washington, D.C. 20006; 887-5872.

*The American Association for Laboratory Accreditation, 2045 N. 15th St., Suite 1000, Arlington, Va. 22201; 528-0072.