Gov. Joseph Teasdale declared a state of emergency yesterday, and ordered 500 National Guardsmen to help provide fire protection in Kansas City during a growing "sickout" by city firefighters.

About 50 to 75 police and firefighters battled a fire that destroyed an unoccupied $5.5 million apartment building on the south side last night. The fire forced the evacuation for a short time of about 100 persons living in a nearby nursing home, police said. Authorities said several persons were sent to area hospitals for treatment of smoke inhalation.

Teasdale said city officials could no longer guarantee the public safety and so the troops would go on duty.

Police have pressed into duty to bolster a firefighting force depleted by firings, suspensions and sickouts as firefighters pressed demands for higher pay.

The governor took the actions after a 45-minute closed-door meeting with Mayor Richard Berkley and a telephone conversation with the head of the firefighters union.

As of yesterday afternoon, police working 12-hour shifts were manning 15 of the city's 33 fire stations and providing protection at five others operated by batallion chiefs. Two stations were closed Wednesday night and early yesterday when firemen failed to arrive for work.

Meanwhile, Atlantic City, N.J., police officers dissatisfied with a 10 percent wage and benefits offer began calling in sick after a court order prohibited large-scale picketing.

Earlier, picket lines set up on highway entrances to the gambling resort had snarled incoming traffic for several hours.