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.