The man, Eero Hiltunen, has admitted the shootings.
The hearing at Hyvinkää District court in hearings was conducted in camera so as not to endanger the preliminary investigation, in which large numbers of people are still to be interviewed, and to protect the privacy of the victims.
Police have not released more information on the case at this point. The investigation is currently focused on interviewing the suspect and eyewitnesses.
A female police trainee injured in the shooting remains in a critical condition in intensive care.
Although four other people are still receiving treatment for their wounds in hospital, two of the injured victims were able to leave hospital on Monday and return home.
The Superpesis Finnish-rules baseball league has agreed to a two-week break for Hyvinkään Tahko before they resume their season on 10 June. The club lost one player in the shooting, and two others were injured.
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