Bank deposits in the District of Columbia soared more than 15 percent in the first quarter of 1978 to a record $4.96 billion compared with $4.3 billion a year earlier, according to a Washington Post survey.

The average growth of deposits at 16 institutions based in the District was somewhat above the 14 percent rate of increase for all 1977, when city banks expanded at a more rapid rate than those based in the suburbs. Moreover, the March 31 figure was higher than the previous record of $4.94 billion last Dec. 31, despite a normal decline in the first quarter each year, as funds are withdrawn to make tax payments.

In the first quarter of 1977, for example, D.C. deposits declined from the Dec. 31, 1976, figure and were up 8 percent over the same quarter of 1976.

Checks cleared by the D.C. Clearing House Association, a sensitive barometer of local business activity, also advanced strongly in the first quarter this year. The total volume of checks cleared was $3,856,726,006.68, up 11.3 percent from $3,464,457,254.12 in the first quarter of 1977. For the month of March alone, check volume qas $1,394,046,812.43, up 10 percent over $1,267,113,269.27.