Hardly anybody is talking about it publicly at the moment, but it's certain to be a hot issue for homeowners in the coming years: property-tax assessments, in the wake of a real estate recession.

Here are the ingredients of a controversy that may well touch you personally:

* Housing prices in most markets around the United States have flattened out in the past 15 months, or have risen only marginally. The days of big, reliable double-digit jumps in home resale values are over, at least for the foreseeable future.

* Local property-tax collections mushroomed during the 1970s, thanks to home assessments that were rising by 15 percent to 20 percent a year in many communities. But that "magic money-machine," as a top Chicago finance official calls it, is about to run out of gas.

* Large numbers of home buyers who purchased near the peak of the price boom in rapidly inflating markets--particularly during 1980--could find their houses over-assessed in the coming 12 to 24 months. Some properties already may be over-assessed, given the financing climate. That fact could force local governments into painful assessment rollbacks, or force the issue into the courts.

Consider this example of the coming tax problem suggested by San Francisco's chief appraiser, Bob Kennedy. The case doesn't involve actual home buyers, but Kennedy says "situations like this already exist here."

Let's say a couple purchased a resale condominium 14 months ago at the height of the city's price spiral for $200,000. The present cash value of that property--absent any special seller financing assistance--might be 10 percent less than the couple paid for it, or somewhere in the $180,000 range.

Yet the assessed valuation for tax purposes would be the full price the couple paid--$20,000 above what it's worth in a market with 18 percent mortgage rates. The couple's condo is over-assessed. And if interest rates stay in the upper teens for another year, the gap could widen further.

At vastly different price levels, similar problems are brewing in markets across the United States, according to tax assessors.

"We're very concerned, I won't try to kid you," said Arthur Murphy, deputy assessor of Cook County, Ill. "There's the possibility of rollbacks in assessments if the sort of market conditions we've been in since 1979 continue for another year or two."

Nearly one-quarter of the city of Chicago's $1.6 billion budget comes from property-tax revenues. Any significant decline in the assessment base's growth would affect the city directly, forcing either tax-rate increases or cutbacks in expenditures.

In Washington, where 25 and 30 percent property-tax increases have been commonplace for the last two years, residential assessor George B. Altoft concedes that the recession "could make assessments a pretty explosive subject." If the sort of automatic annual increases from property taxes the city has gotten used to begin to taper off or go flat, the government "is going to have a very sticky issue on its hands," says Altoft.

Like most cities, Washington's assessment levels lag market trends by more than a year, so the real impact of the price slowdown won't be felt here for another 12 to 18 months. Average prices of home resales in the capital have risen by less than 6 percent this year, and have registered declines in nearly one-third of the city's neighborhoods.

Altoft views the 6 percent nominal price rise as statistical proof that values have actually remained flat. Since the majority of home and condo sales have been at least partially financed with the seller's money, "we've got to discount the true cash price" by 5 percent to 10 percent, he said.

Local property-tax systems differ from state to state and city to city. Your system may have features to it that insulate it from the revenue pressures that Chicago, Washington and others will soon be facing. California homeowners under Proposition 13, for instance, don't experience more than 2 percent annual increases over a base year as long as they live in the same house. (When they sell, the assessment for the new owners jumps to the sale price they paid.)

Some property-tax systems might make things worse for you, rather than better, in the coming year. Denver, for example, uses a 24-month assessment base period that is currently set back in the mid-1970s, when property values began to take off.

As a result, says Denver assessor Michael Licht, homeowners there are going to get whopping property-tax bill increases in the range of 28 percent next year. The tax effects of the current real estate recession (which should mean slower-rising assessment and tax bills in most parts of the county) won't hit Denver homeowners until the late 1980s.