Police arrested Heather Mack, 19, and her boyfriend Tommy Schaefer, 21, on Wednesday after a taxi driver found a battered body in a suitcase outside the St Regis luxury hotel in Nusa Dua, Bali.
The body was identified by hospital officials as Chicago-based Sheila von Wiese-Mack, 62. Neither Ms Mack nor Mr Schaefer has been charged but police have detained them as suspects.
Police chief Djoko Hariutomo said: "We have done blood and psychiatric tests to try to find out their motive in the case, maybe they are mentally unstable. So far we haven't gotten any information on what is behind the murder."
Laughing Ms Mack told reporters "You are crazy" as she walked between rooms in the police station.