In its petition filed before Judicial Magistrate C Kathiravan, police sought custody of two Indians -- Lalit Kumar Gurung, Radhesh Dhar Dwivedi -- and UK national Paul Towers of the ship M V Seaman Guard Ohio for interrogation.
The matter has been posted for tomorrow for hearing.
Police sources said there was a suspicion that certain members of the crew had joined the ship only after it's departure from Kochi and this needed to be probed.
The crew also face charges under the Essential Commodities Act for allegedly buying diesel illegally from local agents.
All the crew members have been remanded to judicial custody and lodged in Palayamkottai Central Prison in neighbouring Tirunelveli District.
Besides the 35 crew, five locals have been arrested and remanded to judicial custody for helping them procure 1,500 litres of diesel illegally.