An 18-year-old man from Whitehaven was questioned after making a racial slur against Deana Uppal on Twitter, the News and Star reports.
He was taken into custody yesterday morning (July 4) on suspicion of a racially-aggravated public order offence. The man has since been released, but the matter has been forwarded to the Crown Prosecution Service.
Deana, who resides in Birmingham, is the current holder of the title of Miss India.
Officers were alerted to the tweet by online racism watchdog Racism Reporter.
Model Deana has already been at the centre of a bullying row after fellow housemate Conor McIntyre threatened to "punch" her.
Conor's behaviour drew nearly 1,000 complaints to TV regulator Ofcom, but producers chose not to eject the contestant after he apologised to Deana.