The District of Columbia government has begun soliciting bids for the design of a computerized nerve system for the 1,250 city intersections equipped with traffic lights. The contract, which is expected to total about $1 million, is an important step toward modernizing the failure-prone signal system, city officials said.

Bids for the year-long design job are due in mid-May. Plans call for installation of new equipment between 1984 and 1987, at a total cost of about $34 million, most of it federal money. However, possible difficulty in obtaining federal funds could delay installation far beyond that date.

According to a consultant's study, drivers and passengers in the District could save 21,000 hours a day, now lost because of delays, and 3 million gallons of fuel a year if traffic flowed more smoothly.

The design contract would provide a blueprint on how to build the new system. Three large computers linked to lights by underground cables would control the signals. Sensors in the streets would monitor traffic flow. Technicians could program complex timing sequences for specific neighborhoods to best handle peak and off-peak traffic there. They could also change timing at individual intersections on command to meet unusual conditions.

The current radio-controlled system, based on 1950s-vintage mechanical technology, is capable of only three basic time sequences and cannot control separate areas of the city individually.

Besides being more flexible, the new electronic system would suffer fewer breakdowns because of the greater reliability of its solid state circuitry, city officials said. Equipment now in place has been badly damaged by weather, collisions and general wear.