Tropical Storm Arlene left one person dead as it swept across Mexico's Gulf coast, but was downgraded to a tropical depression within hours of landfall.

In its path early Thursday, Arlene brought rains from intense to torrential in the states of Tamaulipas, Veracruz, San Luis Potosi, Puebla and Hidalgo, and caused flooding in several cities.

The Red Cross said that a 54-year-old man was electrocuted when he touched a high-voltage power line blown down by the storm in the port city of Tampico, Tamaulipas.

Two other men were reported in critical condition after receiving electric shocks in the midst of the storm as they were repairing an air-conditioning system at a doctor's office in Matamoros, just across the border from Brownsville, Texas.

The emergency services coordinator in Tamaulipas, Pedro Benavides, said that his office remains on high alert Friday, since rains associated with Arlene are expected to continue for at least the next three days.

The overflowing of the Los Remedios River on the outskirts of Mexico City was reported, as well as flooding at 210 spots in the capital.

The weather phenomenon was downgraded to a tropical depression over the Eastern Sierra Madre mountains.

Arlene is the first named storm of the Atlantic hurricane season, which started on June 1 and ends on Nov. 30.