The Montgomery County Council yesterday approved a tax increase of $3.60 a year for each telephone customer line to fund improvements to the county's 911 emergency system.

The increase of 30 cents a month -- which brings the total monthly assessment to 40 cents -- is expected to increase annual revenues from about $350,000 to an estimated $1.4 million. Montgomery County has about 402,558 residential and business telephone customers, and the number is expected to rise to 419,200 in 1987, according to Chesapeake & Potomac Telephone Co.

The additional funds will be used to improve the county's emergency telephone system and to help police officers and firefighters improve response time, County Council member Michael L. Gudis said.

The proposal, recommended by County Executive Charles W. Gilchrist, was approved 4 to 0. Council President William E. Hanna and council members Esther P. Gelman and David L. Scull were absent.

Telephone customers in Prince George's County pay 30 cents a month for the 911 service, while the charge in the District is 16 cents a month. Fairfax County does have a separate tax for its 911 service, but pays for it out of the county's general fund. Fred Kramer, Fairfax County's director of general services, said the charge is equivalent to about 6 cents a month.

"If we want an efficient 911 system, asking taxpayers to pay an additional $3.60 is not exorbitant," said Montgomery council member Rose Crenca.

Montgomery's current 10 cent charge is collected from all telephone customers served by 911, with the revenue used to pay the system's operating and personnel costs. Thirty percent of the revenues from the new 30 cent charge will be used for personnel costs, while the other 70 percent will be used to offset increased operating expenses.

Under the new computerized, state-of-the-art system, the name, address and telephone number of a caller will flash on a computer screen at the county's emergency communications center in Rockville. Dispatchers will know instantly the location of callers having trouble communicating -- such as children who do not know where they live, non-English speaking persons, or ill, frantic or confused callers.