False alarms from more than 1,500 fireboxes in the District have dropped dramatically this fiscal year with the installation of a new telephone call system, replacing the city's old-fashioned pull-lever boxes that pranksters found so easy to set off.

Fire officials say they expect the number of false alarms during this fiscal year to total about 3,700 -- a sharp drop from more than 11,400 false calls during fiscal 1978 and a high of 16,000 during 1972. The fiscal year ends Sept. 30. As of last week, fire officials had reported fewer than 3,600 false alarms since Oct. 1, 1978.

The department receives more than 33,000 fire alerts from the call boxes annually.

The department expects to save thousands of dollars with the new telephone system in addition to lessening the morale-sapping wear and tear on the city's firefighters who must respond to all alarms. Officials said false calls cost the department about $75 for every run the firefighters make.

The telephone box requires the person reporting a fire to open a box, lift the receiver inside and verbally report the fire instead of simply sounding an alarm automatically. The caller's voice is recorded and officials are able to ask questions and try to determine by the person's tone of voice whether the call is genuine. Officials will still be required to send an initial squad car or truck to check suspicious calls.

The telephones are the latest -- and most successful -- effort by the fire department to curb false alarms. Previous efforts have included a variety of anti-prankster efforts.

0fficials tried coating the pull levers on the boxes with dusting power that would show up under a black light. They tried attaching a siren to the boxes to attract attention, and installed cameras in particularly heavy-hit areas of the city to get pictures of the persons pulling the levers. Nothing worked.

In 1972, when the false alarms overwhelmed the department, officials experimented with 111 telephone boxes and found that the false calls were cut from 240 to 12.

About 900 telephone boxes have already replaced old boxes, and the remaining 500 will be changed by December. A full switchover to the system could not be completed until the department's new computer dispatching system was in place.

The phones cost the department about $370 when they were originally purchased. One fire official said they are now worth about $800 each.

James F. Flynn, the department's director of communications, said he hopes to sell the old pull levers as antique souvenirs, and estimated the department could realize about $40,000 from the sale.

Fire officials said anyone convicted of making a false alarm is subject to a fine of $300, a six-month jail term, or both.