I believe you are specifically asking this question to avoid a possible embarrassing translation.
Institute for the Criminally Insane
Most likely means an institute which helps and/or houses the criminally insane
Institute of the Criminally Insane
Perhaps is an institute run by persons who are criminally insane and/or an institute which advances the status of the criminally insane.
The second example is admittedly humorous and is intended to exaggerate the difference in connotation. Your use of either 'of' or 'for' should surely be determined by the context of the actual name it is to be applied to. No doubt someone in your own department's debate has mentioned a similar example to the one I have given.