If the crime game is to not to be a passive 'follow the clues' flavor, but one where the players investigatory actions precipitate (re)actions by the criminals/characters (and thus changing the story and possible outcomes).
Consider the game of chess and how the context of the current board changes what is to happen next. Chess has those fixed and relatively simple rules to resolve the actions of the two opponents (even to how the opponent is likely to decide what to do).
Unfortunately, anything having to do with humans (their complex emotions/motives/interrelations) is magnitudes more complex to try to resolve what 'should' happen next in response to the players actions/reactions. (Likewise the internal state of the characters is far more complex as is the ways they can interact).
Its the old problem games have faced - .you cannot use generalized AI and have to narrow down and choreograph everything (at least as far as some simple generalizations can be utilized in narrow contexts like fight logic).
For 'mind games' I would think that more subtle indicators would be use to try to read the internal mental state of a character versus most games being able to decide by overt actions/motions. Likewise the actions you take will be more mental with any overt actions implying ideas at a character to manipulate them.