Thousands of Maryland home and business owners received notice this week that real estate assessments on their properties will increase an average of 32 percent over the next three years. In some Montgomery County neighborhoods, the increases may be as much as 46 percent.

One of every three homeowners in Maryland is affected by the state government's preliminary property value assessments that are part of a long and complex process by which property taxes will be levied in 1981.

The mailed notices were part of a new method of assessment inaugurated in July 1979 whereby a piece of real estate is assessed only once every three years. Intended to curb patterns of spiraling assessments, the new system was pushed through the Maryland state legislature as part of the so called tax revolt of the late 1970s.

Assessments in Prince George's County did not increase as much as those in the rest of the state, rising 29 percent compared to the statewide average of 32 percent. In Montgomery County, the assessments climbed an average of 37 percent and in the most affluent neighborhoods, such as Chevy Chase, increased as much as 46 percent. a

A family in Bethesda whose home was valued at $100,000 when it was last surveyed two years ago, now will own a house assessed at $137,000 if their rise was the same as the countywide average.

One-third of that increase then would be applied each year, bringing the assessment in 1981 to $112,330. Since, by state law, Maryland residents pay property taxes on 46.825 percent of what their homes are worth, the actual assessed value would be $52,570.

For 1982, he would add another third of the $37,000 rise and do the same calculation. For 1983, he would again repeat the process. At that point the cycle would begin again, with the house being reassessed and the owner adding on a third of the increased value in each of three successive tax years.

The increased assessments translate into more taxes. Two years ago when he was last assessed, the Bethesda homeowner would have paid $1,537 in property taxes. Assuming that today's tax rate remains in force, he will pay $1,839 in 1981, $2,041 in 1982 and $2,243 in 1983.

Many homeowners who have received their assessment notices were dumbfounded by the collection of calculations and terms -- "growth factor," "phase-in-value," for instance -- and began calling tax offices for clarification. "All the phone lines are lit up," said Robert Rudnick, Montgomery County assessments supervisor.

County councillors also got cries for help. "Some Chevy Chase and Bethesda people I've heard from are very, very disturbed" said Rose Crenca, a councilman. With assessment in the hands of state officials, county governments have little power other than introducing counter legislation in Annapolis.

Higher assessments normally -- but not necessarily -- mean higher tax bills. Actual tax rates are set by county governments. Thus, if it chose, a county could offset a doubled assessment by halving the tax rate levied against the owner. Given the rise in local government overhead, few counties can afford such a gift to the taxpayer.

Prince George's County, however, is a special case. There, assessment increases result in the same amount of revenue for the county and lower property taxes for some homeowners.

Unlike Montgomery County, Prince George's officials are bound by the property tax-cutting measure known as TRIM, which provides that the county council cannot collect more money in property taxes than the amount collected in 1979, or $140 million.

One-third of all property units in Maryland were assessed at this time last year. Now the second third (the property units are grouped in geographical groups scattered across the state) are getting their notices. The final third will receive them late in 1981.

Other jurisdictions in the Washington metropolitan area reassess property every year, instead of every three years, as Maryland does.

Homeowners in the District of Columbia received their assessment notices over the summer. Residents of Northern Virginia communities will get theirs early next year.

In Maryland the process begins with state assessors studying the sales histories of particular subdivisions and drawing conclusions on average rises of market values. After door-to-door visits to confirm the physical attributes of a house, preliminary estimates of a market value -- known as the full cash value -- are drawn up.

Rises grow out of normal market appreciation. They also result from new garages and air-conditioners added by owners, condominium conversion and speculation, which now occurs in areas where Metro services is about to begin.

To this full cash value figure, a special ratio -- a complex formula currently has set it at 46.825 percent -- is applied to yield an "assessed value". It is this figure that county government use when actually drawing up tax bills.