Tropical Storm Dolly has dumped rain over Texas and Mexico after pummelling the coast as a category two hurricane a day earlier, leaving widespread floods in its wake.

The Gulf of Mexico's first hurricane of the season ripped off rooftops, shattered windows and toppled trees and power lines, but the storm surge did not cause any breach in south Texas levees as some authorities had feared.

By Thursday morning, winds had weakened to 80km/h and was expected to downgrade again to a tropical depression later in the day, according to the National Hurricane Centre.

No deaths were immediately reported in Texas or Mexico as a result of the storm, though one 17-year-old Texas boy broke several bones when the gusts knocked him out of a seven storey building, US media reported.

The storm dumped 15 to 30cm of rain and cut power to as many as 100,000 people in south Texas late Wednesday.

Texas Governor Rick Perry declared a disaster situation in 15 counties across the southern portion of the state, deploying hundreds of National Guard troops and other emergency crews, local media said.

Jacqueline Bell, who lives on South Padre Island where Dolly made landfall as a category two hurricane packing 160km/h winds midday Wednesday, told CNN the wind had blasted the roof off her neighbour's home.

"When we heard the first bang, I thought it was one of the air conditioners flying ... and then we went outside and we saw the debris," Bell said.

Sixty kilometres to the south, in Matamoros, Mexico, Dolly's winds damaged the city's main water treatment plant, leaving half of the 500,000 inhabitants without drinking water.

The river level in Brownsville, Texas rose steadily but the older levees in the Rio Grande Valley withstood the waters, after some officials had voiced concern that the levees could be overwhelmed.

"Everything is in good shape. We are not experiencing flood conditions in the Rio Grande today," Sally Spener, spokeswoman for the International Boundary and Water Commission, told AFP.

"We do not expect water to be high enough to pose any threat to the levees," she said. "The flooding that they are having is localised street flooding in a lot of communities."