Police made arrests and the case had been referred to Public Prosecution, the Ministry of Interior said in a statement. It did not say how many people were arrested or release any identifying information about those detained.
Patterson went missing after a night out Saturday, and her body was found shortly thereafter. She was a primary school teacher at a British in Doha, and was last seen leaving a night club at a luxury hotel with two men.
British media said her boyfriend initially raised the alarm over her disappearance.
Dennis Rodman pledges to end trips to North Korea
Teacher apologizes for showing sexual image of herself in class