By Sam Karlin

BATON ROUGE, La. (Reuters) - Search-and-rescue operations were still underway on Tuesday in Louisiana, where at least nine people have died in severe flooding that damaged about 40,000 homes, state officials said.

Emergency crews had already plucked more than 20,000 people and 1,000 pets to safety from flooded areas after a storm that broke records for 24-hour rainfall in multiple locations, Governor John Bel Edwards told reporters in Baton Rouge.

Rain-swollen rivers are receding in much of the state, but state officials warned of remaining dangers. Some communities in southern Louisiana could see waters crest later in the week, according to national forecasters.

More than 8,000 people slept in emergency shelters on Monday night, unable to return to their homes, Edwards told a news conference. The state planned to impose curfews on Tuesday night in the parishes with widespread damage.

"This is a historic flooding event," Edwards said of the unnamed storm. "It’s unprecedented."

The storm dumped more than 2-1/2 feet (0.76 meters) of rain on an area near Watson, Louisiana, from Thursday to Monday morning, the highest total reported, according to the National Weather Service.

In Abbeville, Louisiana, a 125-year-old record for 24-hour rainfall was shattered with 16.38 inches (41.61 cm) of rain reported from Friday to Saturday, the weather service reported.

In some water-ravaged areas, houses flooded to rooflines, and coffins floated away. Motorists were trapped on highways. The extent of the damage prompted U.S. President Barack Obama to issue a disaster declaration on Sunday, with additional parishes approved on Tuesday for the federal assistance.

Already, 40,000 residents have registered for disaster aid, Edwards said.

In hard-hit Denham Springs, residents on Tuesday were gutting waterlogged homes, dumping soaked carpets and mattresses.

Sonya Mayeux was still in disbelief. On Saturday, she awoke at 9 a.m. to rising, knee-deep water in her backyard. By 11:30 a.m., the water was nearly above her white SUV.

A neighbor rescued her family by boat. Ultimately, her house flooded nearly to the roof.

“The water just came up so fast,” she said.

"VERY LARGE DISASTER"

Craig Fugate, head of the Federal Emergency Management Agency, told reporters the "very large disaster" was affecting more people than flooding in March that left at least four dead and thousands of homes damaged in Louisiana and Mississippi.

Louisiana will mark the 11th anniversary later this month of Hurricane Katrina, which killed more than 1,800 people when floods overwhelmed levees and broke through flood walls protecting New Orleans on Aug. 29, 2005.

The state's death toll from the latest inundation rose to nine on Tuesday with the discovery of 58-year-old Bill Borne, who officials say drowned near his home in East Baton Rouge Parish. He was founder and former chief executive of Amedisys Inc <AMED.O>, a national provider of home health and hospice care.

In Tangipahoa Parish, authorities believe that a 20-year-old woman found inside her car was killed after her vehicle was washed right off the road, leaving it completely submerged.

A 59-year-old man who died in the same parish appeared to have been swept away by rushing floodwaters.

Many in Louisiana are trying to reach friends and relatives displaced by the storm, the governor acknowledged, noting that most were likely safe but without communications.

"We understand that there are a lot of people who are suffering," Edwards said.

(Additional reporting by Colleen Jenkins in Winston-Salem, North Carolina and Bryn Stole in Baton Rouge, Louisiana; Writing by Letitia Stein in Tampa, Florida; Editing by Tom Brown)