ROCHESTER, N.Y. – A storm blamed for at least 36 deaths across the eastern half of the country spread into the Northeast yesterday, coating trees, power lines and roads with a shell of ice up to a half-inch thick and knocking out power to tens of thousands of homes and businesses.

Ice-covered roads cut into Martin Luther King Jr. holiday observances from Albany, N.Y., to Fort Worth and Austin, Texas, where officials also canceled Gov. Rick Perry’s inauguration parade today because another round of ice was expected during the night.

The weight of the ice snapped tree limbs and took down power lines, knocking out electricity to nearly 70,000 customers in New York state and New Hampshire.

Even in Maine, a state well-accustomed to winter weather, a layer of sleet and snow on roads forced the shutdown of numerous businesses, day care centers and schools.

In hard-hit Missouri, the utility company Ameren said it would probably not have everyone’s lights back on until Wednesday night. Overnight temperatures were expected to drop into the single digits. As of Sunday night, about 330,000 households had no electricity.

Missouri National Guardsmen went door to door, checking on residents, and helped clear slick roads.

About 112,000 homes and businesses blacked out in Oklahoma, some of them since the storm’s first wave struck on Friday, also were still waiting for power yesterday. About 136,000 customers were without electricity in Michigan.

More than 160 flights were canceled at the Dallas-Fort Worth International Airport.

Before dawn yesterday, a car slid into the path of a dump truck on an icy New York highway in Sennett, 20 miles west of Syracuse, killing the car’s driver and two passengers.

“It was very icy, rainy, a snow-sleet mix, so definitely the road conditions had a lot to do with this,” Sheriff David Gould said.

Waves of freezing rain, sleet and snow since Friday had been blamed for at least 15 deaths in Oklahoma, eight in Missouri, five in Iowa, four in New York, three in Texas and one in Maine. Seven of the Oklahoma deaths occurred in one accident, in which a minivan carrying 12 people slid off an icy highway Sunday and hit an oncoming truck.