About 200 placard-carrying Prince George's police officers and firefighters marched briskly in front of the county administration building in Upper Marlboro yesterday to press their request for increased manpower.

The picketing was intended to impress the County Council, which is struggling to set spending priorities in the face of a tight budget proposal from County Executive Lawrence J. Hogan. The proposal is highly controversial largely because it calls for cutting school spending.

The Fraternal Order of Police says the county has 1.2 police officers per thousand residents compared to the national average of 1.7 for a suburban county or 2.2 for an urban area and that response time to calls for aid in the county has increased from between 3 to 5 minutes to over 7 minutes as the number of calls has increased.

Professional Firefighters Association pickets said Prince George's has only half the number of uniformed firemen per capita that Fairfax, Montgomery or largely rural Anne Arundel County have and there is a high rate of undermanned calls.

Hogan's budget asks for 50 more police officers, 25 more firefighters and 11 ambulance technicians. The unions say this is too few.

Police Chief John E. McHale and Fire Chief Marion Estepp agree that they need more men, but, as Hogan appointees, they accept his contention that Prince George's must live within its means.

"Prince George's County, the last time I looked, was the 22nd richest in the nation," said Estepp. "Montgomery is number one and Fairfax is close. We just don't have that kind of money." He pointed out that Prince George's depends on a larger force of supplementary volunteer firefighters than the other counties.