HOUSTON — Five days after the pummeling began — a time when big storms have usually blown through, the sun has come out, and evacuees have returned home — Tropical Storm Harvey refused to go away, battering southeast Texas even more on Tuesday, spreading the destruction into Louisiana and shattering records for rainfall and flooding.

Along 300 miles of Gulf Coast, people poured into shelters by the thousands, straining their capacity; as heavy rain kept falling, some rivers were still rising and floodwater in some areas had not crested yet; and with whole neighborhoods flooded, others were covered in water for the first time.

Officials cautioned that the full-fledged rescue-and-escape phase of the crisis, usually finished by now, would continue, and that they still had no way to gauge the scale of the catastrophe — how many dead, how many survivors taking shelter inland or still hunkered down in flooded communities, and how many homes destroyed.

For everybody, it was another head-shaking 24 hours:

• The storm made its second landfall early Wednesday morning in Louisiana, just west of the town of Cameron, the National Hurricane Center announced at 4 a.m. As Harvey moves northeast through the state scarred by Hurricane Katrina in 2005, forecasters expect it to gradually weaken and become a tropical depression by Wednesday night.

• Local officials in Texas said at least 30 deaths were believed to have been caused by the storm through Tuesday, up from eight a day earlier. The dead included a Houston police officer, Sgt. Steve Perez, 60, who was caught in flooding on Sunday while trying to report for duty. “I expect that number to be significantly higher once the roads become passable,” said Erin Barnhart, the chief medical examiner for Galveston County.

• The city of Houston imposed a curfew from midnight to 5 a.m., starting Tuesday night and continuing until further notice. The curfew was requested by the Houston Police Department, partly in response to reports of “small-scale looting” and other crimes, Chief Art Acevedo said at a news conference Tuesday evening. He added that the curfew would help search and rescue teams get around without interference.

• Parts of the Houston area broke the record for rainfall from a single storm anywhere in the continental United States, with a top reading on Tuesday afternoon, since the storm began, of 51.88 inches in Cedar Bayou, east of Houston, the National Weather Service reported. The previous record was 48 inches in Medina, Tex., from Tropical Storm Amelia in 1978, and with the rain still falling along the Gulf Coast, Harvey could top the 52 inches recorded in Kauai, Hawaii in 1950 from Hurricane Hiki.

• Houston officials had at first limited the city’s main shelter, the George R. Brown Convention Center, to 5,000 evacuees, but by Tuesday morning it had swelled to more than 9,000, with more arriving by the hour, Mayor Sylvester Turner said. By the evening, evacuated residents were setting up cots in corridors because they said the main dormitories were uncomfortably crowded.

One of the people bunking at the convention center, Keimaine Percel, a mechanic, had not seen his home since it flooded, but he was trying not to think about it. “I heard it was real bad,” said Mr. Percel, 35. “I don’t know unless I get back.”

The Red Cross said that in Houston alone, 17,000 people began their day Tuesday in shelters, and the numbers were rising there and in inland cities that had taken evacuees such as Dallas, San Antonio and Austin. Mr. Turner said Houston would create new shelters, Dallas opened its convention center on Tuesday as a shelter for 5,000 people, and Fort Worth said it would open shelters, as well.

In the Kingwood neighborhood of Houston, people waved towels from apartment windows and yelled “we’re here” and “family of three needs help,” hoping to draw one of the volunteers piloting fishing boats, inflatable rafts and kayaks.