Washington area residents, seeking lower taxes and cheaper housing, are rapidly turning Anne Arundel County into a suburd of Washington, a study done for the county has found.

Although the county is still classified by census takers as part of the Baltimore metropolitan area, three times as many new residents are moving there from Washington as from Baltimore, the study found.

The results reflect profound changes in the county on the Chesapeake Bay caused by the new migration patterns of Washington area jobholders who are moving into areas farther removed from their "home" city.

The patterns emergin from the consultant's report, based on a survey of nearly 500 new residents, present Anne Arundel with potential problems in years ahead, county officials said. The influx of higher-income Washingtonians has already helped to inflate housing prices and to create the need for new county services, county officials said.

Homeowners used to paying the higher prices in the Washington market and willing to pay equivalent amounts in Anne Arundel tend to inflate housing costs in their new communities. Often newcomers move into new subdivisions, creating by their very presence a need for new schools, sewage treatment plants and trash collection - all items paid for by taxes.

"Our real challenge," County Executive Robert A. Pascal said yesterday, "is going to be to maintain our tax posture, to maintain services and not lose the quality of life. That's saying a whole lot."

So far, Pascal said, increased tax revenue from new residents has outweighed any drain on the county treasury. Within the limits of county plans for controlled growth, he said he welcomes the newcomers.

"Honestly and truly," he said, "the relaxed atmosphere in which Anne Arundelans move about is very appealing compared to the more formal in places like Montgomery County."

The report provides the most extensive documentation to date of a trend recognized by the Metropolitan Washington Council of Governments in a February 1977 report. That study showed that 23,000 new people had moved to Anne Arundel between 1970 and 1975.

The county's population has grown from just under 300,000 in 1970 to nearly 400,000 today.

In the new study, a better life style scored second to affordable housing as the reason cited by Washingtonians who bought single family homes in Anne Arundel. It is a lifestyle, some fear, that could change with their increased presence.

"I would hope we can keep some of Kurdle, Anne Arundel County planthe rural atmosphere," said F. Beck ing and zoning director. "All the reasons why people want to move here being changed by their moving here is almost impossible to resolve. The solution is to pace development."

The Washington market, the study found, now includes the county's entire southern portion and extends five miles north of Route 5 - the controlled-access highway connecting Washington and Annapolis - as far as Severna Park.

An average of 61 percentage of single-family home buyers and 75 percent of town house buyers in this area work in the Washington area, according to the telephone survey conducted last December.

A great number of these new county residents had moved from Prince George's County and were often former renters buying their first homes or homeowners trading up, the study showed.