HONOLULU (AP) _ An 11-year-old Vietnamese girl who wrote an essay that called America ''a place that lends a hand to those in need'' won a trip to the Statue of Liberty rededication, but the $9,000 car she also won could cost her fatherless family its welfare benefits.

Hue Cao, a sixth grader, won first prize in a contest sponsored by the Aloha Liberty Foundation. The prizes are a trip to New York City for the July 4 festivities and a 1987 Nissan Sentra XE.

''America is a place that lends a hand to those in need. The Americans care for all people, from homeless to helpless people,'' she wrote in her essay about the Statue of Liberty and freedom.

A little more than an hour after Cao was presented with the prizes on Tuesday, her family was called by a welfare worker who had seen her picture in the Honolulu Advertiser. If Cao's mother accepts the new car, the family will lose all its welfare benefits, the welfare worker told the family.

Lien Ma, a widow who fled Vietnam with her family in a small fishing boat in 1979, is supporting Cao and two sons, Thai, 16, and Quang, 14. Four other children, ages 18 to 24, are supporting themselves.

The family receives $546 a month in financial assistance, $352 in food stamps and Medicaid health coverage.

Under federal regulations, families cannot receive welfare benefits if they have more than $1,500 in resources, according to state welfare administrator Shig Nakashima, who said a $9,000 car would be counted as a resource.

Cao's trip is not in jeopardy because it cannot be converted to cash, Nakashima said. ''It's strictly the regulation that applies to everyone, not only in Hawaii, but across the country.''

The family's welfare benefits are safe for now because Mrs. Ma has not signed papers accepting the car. She planned to do so in July when Cao returned from New York, said Paulette Moore, Cao's teacher at Waipahu Elementary School.

Aloha Liberty Foundation president Reg Schwenke said he plans to ask President Reagan for a waiver to allow Cao's family to keep the car without losing its benefits. If Reagan can't solve the problem, Schwenke said he would explore other avenues.

''Here's a girl who's discovered that anything is possible in America, and we at the foundation will not do anything to dispell that notion,'' he said.

Mrs. Ma didn't like the idea of calling Reagan. ''We don't like to bother him. It's too humbug,'' she said through her daughter, Trinh.

One idea endorsed bu Cao's mother is for the foundation to accept the car, auction it off and use the proceeds to establish an educational trust Cao can draw from after she turns 18.