The two reports, made on Jul 4 and Jul 5, were in relation to comments allegedly made by Ms Khan on social media, said the Singapore Police Force (SPF) on Sunday (Jul 5).
"She allegedly commented that Singapore law enforcement authorities discriminated against citizens, and that compared to other groups, rich Chinese and white people were treated differently under the law.
"In the context of a news article on the City Harvest Church ruling, Raeesah Khan allegedly commented that Singapore jailed minorities mercilessly, harassed mosque leaders but let corrupt church leaders who stole S$50 million walk free, and questioned who had been paid," said SPF in a statement.
"The Police have consulted the Attorney-General’s Chambers, which advised that an offence of promoting enmity between different groups on grounds of religion or race under Section 298A of the Penal Code is disclosed," the statement said.
Police investigations are ongoing.
The offence of promoting enmity between different groups on grounds of religion or race under the Penal Code carries an imprisonment term of up to three years or a fine, or both.