Miami ? A boat overloaded with Cubans being smuggled into the U.S. tried to ram a Coast Guard vessel in rough seas early Saturday, and a woman aboard the boat died, authorities said.

The 36-foot, go-fast boat ignored orders to stop when the Coast Guard tried to intercept it 4 miles south of Boca Chica about 6:30 a.m., said Petty Officer James Judge, a spokesman for the Coast Guard.

Coast Guard crew then fired two shots into the vessel’s engine to disable it, he said.

“The boat was bouncing around like crazy. It was very rough, choppy waters,” Judge said. “They repeatedly attempted to ram the vessel more than five times, but they never made contact.”

The boat carried 31 Cubans and three people authorities said were smugglers.

The woman who died suffered a head injury and severe bruising to her face, and an autopsy was scheduled for today.