Miss Moceanu, whose parents are from Romania, was the youngest member of the US gold-medal-winning team at the 1996 Olympic Games in Atlanta, and in August she became the first non-Russian to win the all-round gymnastics competition at the Goodwill Games in New York.
Miss Moceanu has been in hiding for the past week since she left home saying that she was going to a shopping centre nearby in Houston.
A week ago, a lawyer initiated papers with the court in Houston stating her intention to seek adult status and an order preventing her parents from contacting her before a full court hearing on 11 November. The first hearing of her case was scheduled for yesterday.
In an interview with the Houston Chronicle, Ms Moceanu said her father, Dumitru, had forced her to follow a punishing training regime that excluded all else, and occasionally hit her.
She also accused him of trading on her name and squandering her earnings on the $4m private gym he built and runs, a sportswear business, and a series of risky investment projects.
Dumitru Moceanu denies any wrongdoing and last week made an emotional appeal for her to return. Her mother, Camelia, went on television yesterday to say that their home was always open for their daughter.
In a statement issued through her lawyer, Miss Moceanu said: "I want whatever I have earned to be under my control so I know how my earnings are being used, and I want to be able to train and compete in the sport I love ... because I love it, not because my father tells me I have to make more money."