National Savings and Trust will no longer return canceled checks to customers with interest-paying Super NOW accounts, in what appears to be the first such move by a major bank in the District.

Instead of canceled checks, customers will receive a statement listing deposits and withdrawals under NS&T's check "safeguarding" program. The change will not affect customers with regular checking accounts, who will receive both canceled checks and monthly listings of transactions.

Vice President David S. Smith cited costs as the reason for the decision to truncate the check-return process. He also said industry studies show the majority of customers have no objection to a statement once they get used to it. NS&T conducted a test of the program with its employes before extending it to NOW (Negotiable Order of Withdrawal) accounts.

With financial institutions being compelled to pay market rates on checking as well as savings accounts, cost-cutting measures such as this are likely to become more widespread, banking officials say.

NS&T's NOW account carries a monthly service charge of $6 regardless of the balance. Checks are microfilmed and stored at the bank for seven years and customers are entitled to one free photocopy of a check per month, or 12 per year. Additional photocopies cost $1 each.

The canceled check has traditionally been considered proof of payment. However, the Internal Revenue Service, in recognition of developments within the industry, has instructed auditors to accept bank statements in most cases. Spokesman Larry Batdorf explained that if the taxpayer has another item lending veracity to the claim, it is more likely to be accepted than if the taxpayer has many unsubstantiated items.

For example, a physician's bill of $312.13 dated Jan. 7 submitted with a bank statement showing a like amount taken out of the account Jan. 12 would probably be accepted. However, if the claim is over $1,000, a photocopy of the check may be required. On the other hand, if many items cannot be substantiated, a photocopy of a $15 check might be required.

Proponents of check "safekeeping" or truncation claim that it ends the headache of balancing the checkbook and that most credit card companies no longer return original receipts. Consumer groups have sought to block widespread adoption of the practice of not returning canceled checks because they believe the owners have a right to, and a need, for them.

According to Transdata Corp. of Cambridge, Md., a research consulting company specializing in banking, the percentage of institutions using safekeeping has remained at just under 10 percent for the past two or three years. It is less common with banks (8 percent) than with savings and loans and mutual savings banks (up to 36 percent).

A Washington Post survey of 20 area institutions revealed that just one other bank, Citizens Bank and Trust, and four savings and loans no longer return checks. Three institutions offer a choice. In some cases there is an extra charge for check return. In percentage terms, the figures tally with a 1982 survey by the U.S. League of Savings Institutions showing that 55 percent return checks, 15 percent keep them, and 30 percent offer customers a choice.

Customer surveys show concern about the cost and nuisance of getting photocopies when needed. A 1980 Unidex survey of consumer attitudes found that 43 percent found the concept "very unattractive," whereas just 15 percent found it "very attractive." The experience of federal credit unions, which have been required by law to truncate share drafts (checks) since 1974, shows that only one copy is requested for every 3,000 checks cashed, according to the Credit Union National Association.

The American Bankers Association says statistics on how much money banks save through safekeeping are proprietary information. The Federal Reserve Bank of Atlanta estimates the average cost of check processing at 42 cents per item, yet banks charge only between 12 and 17 cents per check. If half of all interbank checks were truncated, a savings of five cents per check would result, Transdata estimates.

The experience of Valley National Bank in Phoenix, the 28th largest in the country, convinced it of the value of safekeeping. Back in 1975 it projected check processing costs, which then totaled $5.5 million, would escalate to $17 million a decade later. In May 1981 it found truncation of 45 percent of its accounts saved $2 million annually. It received just one request for a photocopy for every 1,500 checks stored.