Profits of National Bank of Washington tumbled sharply in the third quarter, mainly because of losses associated with a "check-kiting" scheme in which principal owners of the now-defunct Boss & Phelps real estate firm wrote millions of dollars of worthless checks.

Separately, United Services Life Insurance Co., Financial General Bankshares Inc., Bank of Virginia Co., First Maryland Bancorp and several other area bank firms reported increased profits for the first nine months of 1981, generally a lackluster period for the nation's financial services and insurance industries.

At NBW, the city's third-largest bank, July-September profits plummeted to $272,995 (20 cents a share) compared with $1.34 million ($1) in the same period last year. The weak performance in the recent quarter also accounted for most of a substantial decline in profits for the first nine months of the year to $1.82 million ($1.32) from $3.26 million ($2.37) in the comparable 1980 months.

Earlier this week, two Boss & Phelps executives were sentenced to six months in prison each as a result of obtaining $900,000 through false checks drawn on NBW and First American Bank accounts. NBW Chairman Luther Hodges Jr. said yesterday that his bank suffered a one-time "fraudulent use of funds" loss of $560,000 in the third quarter--most of it related to the Boss & Phelps situation but also including several counterfeit certificate cases.

In addition, the bank suffered in the quarter from record interest rates, which encouraged customers to withdraw funds from low-yielding accounts to invest in money market mutual funds or money market certificates, leading to higher interest costs for the bank.

Hodges said in an interview that he doubted any security system could have caught the schemes that resulted in extraordinary losses in the quarter, but he noted that NBW has installed even more safeguards. He also forecast a rebound in earnings during the fourth quarter to levels earlier in the year, as the bank continues to recover from a troubled period of bad loans and management problems in 1979-80.

At the same time, assets, deposits and loan volume are increasing. As of Sept. 30, assets reached a record $941 million and deposits increased to $715 million from $651 million a year ago. Loan volume expanded to $543 million from $511 million, with most of the increases in regional business and international lending, Hodges stated.

United Services Life earnings from insurance operations rose 32 percent in the third quarter to $3.4 million (62 cents a share) from $2.7 million (47 cents) a year earlier. For the first nine months, the International Bank of Washington affiliate reported operating earnings of $10.3 million ($1.81) versus $9.7 million ($1.71). Including capital gains, net income rose to $11.3 million ($2.01) from $9.7 million ($1.72), a gain of 16 1/2 percent.

New life insurance sales totaled $461 in the recent quarter, up 49 percent from the same period last year, while new life sales for the first nine months was $1.27 billion, a 46 percent gain. Life insurance in force topped $8 billion on July 27, some 16 months after it reached $7 billion.

United Services also declared a cash dividend of 25 cents a share on common stock, payable Nov. 16 to stockholders of record Nov. 2. The company, of which International Bank owns 36 percent, sells insurance to military service officers and their families through three subsidiaries as well as to the general public through Bankers Security Life, another subsidiary.

Financial General Bankshares, a bank holding company for the First American banks and other financial institutions, reported third-quarter profits before gains or losses from selling securities soared 49 percent to $5.8 million (80 cents a share) from $3.9 million (53 cents) a year ago. Net income, including securities transactions, was $5.83 million (80 cents) versus $3.94 million (54 cents).

Nine-month operating earnings rose 36 percent to $15.96 million ($2.19) from $11.75 million ($1.61) while net income was $15.91 million ($2.18) versus $11.72 million ($1.61). Earnings for the quarter and nine months were at record levels, which Chairman B. Francis Saul II attributed to an ability to maintain liquid assets (readily converted into cash for immediate investment) during a period of high interest rates that depressed profits at many bank firms.

Net interest income in the quarter rose 22 percent, for example. Assets rose 9 percent in the past year to $2.58 billion on Sept. 30, while deposits at the company's dozen banks climbed 8 percent to $2.13 billion. For the nine months, the return on stockholders' equity (stock investments) was 14.6 percent compared with 11.9 percent in the 1980 period, Saul said. Investors from the Middle East are in the final stages of preparing a takeover bid for the Washington firm.

First Maryland Bancorp of Baltimore, the holding company for First National Bank, reported third-quarter operating earnings of $5.87 million ($1.14 a share) compared with $5.39 million ($1.03) a year earlier. Nine-month operating earnings increased 8 percent to $17.51 million ($3.40) from $16.51 million ($3.14), while net income rose to $17.23 million ($3.34) from $16.18 million ($3.08).

Assets on Sept. 30 were $2.8 billion compared with $2.47 billion a year ago. Deposits rose to $2.07 billion from $1.82 billion, while loan volume increased to $1.64 billion from $1.5 billion. On Sept. 4, First Maryland acquired First National Bank and Trust of Western Maryland.

Bank of Virginia Co., based in Richmond, reported third-quarter income before securities transactions rose to $4.2 million (75 cents a share) from $3.713 million (68 cents) for the same quarter of 1980.

Earnings for the nine months before securities transactions amounted to $11.1 million ($1.98) compared with $10.5 million ($1.93) for the same period a year before.