BOWLING GREEN, Ky. (AP) _ High wind or tornadoes shattered the domed glass roof on a shopping mall and caused widespread damage in residential areas today as a strong storm system rumbled across Kentucky.

Two deaths were reported, one elsewhere in Kentucky and one in Tennessee.

The Greenwood Mall, Bowling Green's largest, had just opened for the day when it was struck by a thunderstorm, part of a weather system extending across much of the South and Midwest, police reported.

Police had no reports of serious injuries at the mall, which contains 78 stores.

A woman in Hardin County, in central Kentucky about 60 miles north of Bowling Green, was killed when high wind overturned her trailer home, state police said.

The thunderstorm, with a series of small tornadoes, hit the area about 10 a.m., the National Weather Service reported. The weather service could not confirm whether the tornadoes touched down at the shopping center.

''I was just coming in the door and I heard glass crash, and the wind started blowing and I just hit the floor,'' said Frances Graham, who works at the Greenwood Mall.

''It broke all the car windows out of our cars out front, and I really don't know what the extent of the damage is. They're asking us now to get out of the mall as quickly as possible for fear of a gas leak.''

The storm also damaged business and residential areas of Bowling Green, overturning cars and mobile homes, said Jim Burch, Warren County's disaster and emergency services director.

Elsewhere in western and northern Kentucky, thunderstorms downed trees and power lines and damaged homes and farm buildings in several counties, authorities said.

The Kentucky thunderstorms were part of a large weather system that scattered stormy weather from the Gulf Coast to the Great Lakes.

High wind damaged mobile homes and injured two people in Illinois, and scattered tornadoes in Indiana damaged trees and several farm buildings and injured two people in a mobile home, state officials said.

One man was found dead underneath his house after a string of tornadoes swept across southeastern Tennessee, state officials said. Several homes were damaged and two people were injured.

Severe thunderstorms also hit southwestern Ohio at noontime, but no funnel clouds touched down. Cincinnati Gas & Electric Co. said about 7,000 customers were without power in southwestern Ohio and northern Kentucky.