A teenage girl who was dropped from her high school's cheerleading squad after refusing to chant the name of a basketball player who had sexually assaulted her must pay compensation of $45,000 (£27,300) after losing a legal challenge against the decision.

The United States Supreme Court on Monday declined to hear a review of the case brought by the woman, who is known only as HS. Lower courts had ruled that she was speaking for the school, rather than for herself, when serving on a cheerleading squad – meaning that she had no right to stay silent when coaches told her to applaud.

She was 16 when she said she had been raped at a house party attended by dozens of fellow students from Silsbee High School, in south-east Texas. One of her alleged assailants, a student athlete called Rakheem Bolton, was arrested, with two other young men.

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In court, Bolton pleaded guilty to the misdemeanour assault of HS. He received two years of probation, community service, a fine and was required to take anger-management classes. The charge of rape was dropped, leaving him free to return to school and take up his place on the basketball team.

Four months later, in January 2009, HS travelled to one of Silsbee High School's basketball games in Huntsville. She joined in with the business of leading cheers throughout the match. But when Bolton was about to take a free throw, the girl decided to stand silently with her arms folded.

"I didn't want to have to say his name and I didn't want to cheer for him," she later told reporters. "I just didn't want to encourage anything he was doing."

Richard Bain, the school superintendent in the sport-obsessed small town, saw things differently. He told HS to leave the gymnasium. Outside, he told her she was required to cheer for Bolton. When the girl said she was unwilling to endorse a man who had sexually assaulted her, she was expelled from the cheerleading squad.

The subsequent legal challenge against Mr Bain's decision perhaps highlights the seriousness with which Texans take cheerleading and high school sports, which can attract crowds in the tens of thousands.

HS and her parents instructed lawyers to pursue a compensation claim against the principal and the School District in early 2009. Their lawsuit argued that HS's right to exercise free expression had been violated when she was instructed to applaud her attacker. But two separate courts ruled against her, deciding that a cheerleader freely agrees to act as a "mouthpiece" for a institution and therefore surrenders her constitutional right to free speech. In September last year, a federal appeals court upheld those decisions and announced that HS must also reimburse the school sistrict $45,000, for filing a "frivolous" lawsuit against it.

"As a cheerleader, HS served as a mouthpiece through which [the school district] could disseminate speech – namely, support for its athletic teams," the appeals court decision says. "This act constituted substantial interference with the work of the school because, as a cheerleader, HS was at the basketball game for the purpose of cheering, a position she undertook voluntarily."

The family's lawyer said the ruling meanst that students exercising their right of free speech can end up punished for refusing to follow "insensitive and unreasonable directions".

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