A woman who allegedly told police that a man had threatened to set her on fire if she did not take off her hijab was not telling the truth, according to police.

The alleged incident took place on the University of Michigan campus three days after Donald Trump was elected. She said she was set free after taking off her hijab in front of the man.

Police worked with the FBI and the state police to investigate what appeared to be a hate crime. They conducted witness interviews and reviewed surveillance footage of the area.

The University of Michigan issued a campus safety alert and students told local news outlets that they felt “disgusted” and “angry”.

The woman gave numerous inconsistent statements, however, police in Ann Arbor said. Detectives then concluded that the incident did not occur.

It is unclear whether the woman will face charges. Ann Arbor police could not be immediately contacted for comment. The woman's identity has not been disclosed.

The news comes shortly after a New York student was charged with obstruction and false reporting of a crime after she said that three white, drunken men called her a “terrorist” on the subway as bystanders watched and did nothing.

The men, she said, tried to pull her hijab off her head.

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Police found there were no witnesses or video evidence to support her claims and after several weeks the alleged victim recanted. She could face up to one year in jail.

Despite the two allegedly fabricated encounters, there has been a spike in reported hate crimes and attacks in the months leading up to and after the presidential election.

President-elect Trump has used heated rhetoric against Muslims, ethnic minorities and immigrants, pledging to build a wall along the US-Mexican border, banning Muslims from entering the US and forcing American Muslims to sign a registry.

The FBI found there was a 67 per cent increase of anti-Muslim incidents in 2015.