Disarray that apparently verged on chaos overtook the District of Columbia's property tax collection system during the past year.

Thousands of bills were not sent when due; thousands of payments that were made have not been recorded.Refunds due to thousands of property owners did not get paid. Savings institutions throughout the metroplitan area, including the biggest ones in Washington, reported unprecedented difficulties in obtaining accurate bills for their borrowers and in getting payments credited once they were made.

Complex new property tax legislation, computer failures and an acute shortage of staff at the District's Department of Finance and Revenue combined to throw the tax records into disorder. Whether the city actually lost money as a result is not clear, because while some tax bills were held up and payments delayed, other taxpayers were billed for more than they actually owed.

Carolyn Smith, director of Finance and Revenue, acknowledged in an interview that the tax system faltered badly last year. She said, however, that new procedures developed by private consultants had enabled the department to bring the problems under control, so that "this year, 1981, is supposed to be completely clean. We believe the '81 bills are as pure as can be." Last year's problems, she contended, were a "one-time only" phenomenon.

Her optimism is not shared by tax officers at the major savings and loan institutions, who are responsible for paying tens of thousands of tax bills for their borrowers each year. Without exception, tax officers interviewed during the last two weeks said the District was by far the worst jurisdiction in the Washington area at maintaining accurate property records and collecting accurate bills. They rated Fairfax County and Prince George's County the best, and agreed that the District was, as one of them put it," "at the bottom of the totem pole."

Collection of taxes on the city's 147,000 taxable parcels of real estate is an essential function of the District government. The property tax yields about $200 million a year in revenue, or 20 percent of all city tax revenue, and properties on which taxes are delinquent can be sold at auction.

This year's sale, affecting some 3,800 properties, is scheduled for tomorrow morning. Smith said that "as bad as 1980 was" in her department, "we were very pleased with the accuracy of the tax sale listings. We think we have done a superb job of getting this information together."

Smith became director of the department 13 months ago, when the seeds of trouble had already been planted. "One of the first things I was told was, look out for the tax assessment section, you have trouble there," she said. The prophecy was accurate. According to information compiled by savings and loan tax officers, city employes, private consultants and disgruntled individuals, incidents such as these were common:

All payments had to be "posted," or recorded, manually when the department's computerized system failed. Harassed clerks had to enter by hand on a master list each payment, the amount, the date and the property involved -- a process that inevitabely fell far behind, since 30 of the 490 positions in the department are vacant. Several thousand tax bills that were paid last March have still not been posted and the taxpayers are theoretically delinquent, according to department workers. A tax officer at First Federal Savings and Loan said he did not receive bills for taxes due in March until May, and then he "went down there in November and they were still hand-posting the payments. Names were being put on the delinquency list by one part of the organization while the payments had been made and they were being hand-posted by another part."

American Federal Savings & Loan, which has recently merged with Perpetual Federal Savings and Loan, the city's largest savings institution, received only half the bills for the 2,000 District properties on which it holds mortgages and expected to pay the semiannual tax installment last March. "That meant we couldn't send payment because we didn't know the amount," said tax officer Alice Kirkley. "We wrote to ask for the bills, we asked for an extension of time to pay them, and we asked for the bills again, and some of them still wound up recorded as delinquencies." She said she and a colleague "took a quick keypunch course and we keypunched a tape with an accurate listing of our accounts and sent it to them. We were doing their work for them, but we still could not get the bills."

American Federal was not alone. A tax-processing service that handles accounts for several major S&Ls reported that 2,800 of its 40,000 anticipated bills failed to arrive in March. At National Permanent Savings & Loan, tax officer Carolyn DeCao said, "I have on my desk cards for properties on which the taxes due in September have not been paid and the city knows they have not been paid, because we can't get the bills." At another savings institution, the tax officer, who asked not to be identified, said he still had not received September bills for more than $75,000 worth of taxes he knows are due.

Last Jan. 30, American Federal delivered to the tax office a check for $8,923.19 in back taxes on several properties. A Finance and Revenue clerk signed a receipt for the check the same day, but it was not deposited in a bank until July 26. At Community Federal Savings & Loan, one of the city's smallest, President Orlando Darden said that in December he sent a duplicate tax check to replace one delivered in March and never cashed by the city. "There is a problem down there and it appears to be getting worse," Darden said.

Savings institutions were billed for taxes on properties on which they had closed their accounts as long ago as three years.

Receiving a tax bill for one of its borrowers, Perpetual paid the money, but when it charged the deduction to the man's escrow account, it found the account $30,000 short of funds. The man, who owns a condominium had been billed for the taxes on every apartment in his building, not just his own. Officials of several S&Ls said it was not unusual for the Finance and Revenue Department to do that. Director Smith and her associate director, Faith McDonald, confirmed that this occurs, but they blamed developers who, they said, often juggle apartment numbers several times when converting a building from rental units to ownership.

Several tax officers said that the District's records failed to keep up with the trend among some property owners to combine lots to maximize the benefits of the so-called homestead exemption, which exempts from taxation $9,000 of the assessed valuation of owner-occupied single-family homes. Several hundred property owners whose houses stand on double lots have combined the lots into one, to get the lower residential tax rate on the entire property, and not be taxed at the commerical tax rate on a vacant lot. The city, which bills for taxes according to square and lot number, continued to bill for, and collect on, the old lot numbers, while the new lot numbers were recorded as delinquent.

McDonald, Smith's associate director, said that since 98 percent of the lot changes are made at the request of the property owner, it is the responsibility of the owner to notify Fiance and Revenue and the mortgage holder of the new designation. But clerks in the Finance and Revenue office say that even if the taxpayer does send in a written notice of a lot change, the job of the person who records those changes on the tax records has been vacant since July.

Because the homestead exemption law was enacted shortly before the September 1979 tax bills were processed, many eligible properties were not approved for the exemption in time for that billing period. As a result, the owners were billed for the taxes at the full rate, with the understanding that the overpayments would be refunded later. Tax officers at the savings institutions say many of their clients are still waiting for the refunds.

Also entitled to refunds and not getting them are the uncounted persons who pay taxes twice on the same property. That happens because their mortgage lender pays the taxes when they are due out of escrow funds collected in the homeowner's monthly payment, and the homeowner, notified of that on a form that looks like a tax bill but is marked "this is not a bill," also pays.

Smith said that personnel shortages in her department "do hinder our ability to process refunds, but refunds are not at the top of our priority list."

Independent sources familiar with the workings of Smith's department said Finance and Revenue was apparently overwhelmed by several things beyond its control that happened at once. The City Council enacted the homestead exemption and multiple real estate tax rates for different types of properties, condominium conversions multiplied, the computerized record system fell apart when key employes left abruptly and a hiring freeze imposed by Mayor Marion Barry to save money left important positions vacant. Smith said she is now "recruiting vigorously" to fill vacant positions -- but Barry's proposed budget for the fiscal year that begins next Oct. 1 calls for a further reduction of 85 positions at Finance and Revenue.

Smith said that new procedures for tax billing developed by the accounting firm of Coopers & Lybrand are now "on line" and should prevent a repetition of last year's difficulties.

But in the meantime, the reality of the tax records confusion is epitomized by the scene in Room 1145 of the Municipal Center -- Assessment Services Division, Accounts and Control Section, the front lines of the property tax battle. Records and documents are piled high on desks and dumped into cardboard boxes; clerks on their hands and knees rummage through piles of plastic trays and cartons jammed with files and bills. A cardboard box marked "trouble" is filled to overflowing.