(Updates with additional deaths, adds byline)

By Bruce Nichols

HOUSTON, Aug 16 (Reuters) - At least four people died on Thursday as Tropical Storm Erin swept into Texas with heavy rains that caused flooding, traffic tie-ups and a fatal roof collapse.

Up to eight inches of rain fell across Houston, where street flooding brought traffic to a standstill on several major highways after the storm came ashore 175 miles (281 km) to the southwest, near the seaside city of Corpus Christi.

The rains were blamed for a roof collapse at a grocery story that killed one person and injured another, said Houston Assistant Fire Chief Jack Williams.

In Comal County in central Texas, the Texas Department of Public Safety said three people were killed in a head-on car crash blamed on wet roads.

As Erin, which had peak winds around 40 miles per hour (64 km) before coming ashore from the Gulf of Mexico, moved through the state, there were numerous reports of closed roads and people needing rescues from flooded cars.

Houston television reports showed neighborhoods where streets were filled with water and people waded through waist-deep water.

Houston is a big refining and petrochemical center but companies said operations had not been affected by the storm.

(Additional reporting by Jim Forsyth in San Antonio)

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