Professor takes our money and goes incommunicado, do we complain to the department or the police? Several years ago an academic publisher I worked for were setting up a new journal. We approached the prospective editor-in-chief, lined up some plans for the first issues, signed a contract, and paid him the first installment of his honorarium. Then he ceased being contactable. We knew he's still alive &amp; active because he was writing papers, supervising students and attending conferences, but he didn't answer our emails and phone calls.

If we had chosen to pursue the matter then, should we have taken it up with his department/university/research institute, or with the police?

If it matters, the prospective editor-in-chief is from India.
Obligatory disclaimer: I am not a lawyer...

This sounds like a contract dispute: whether the editor has discharged his side of the agreement. As such it is likely to be a civil matter rather than a criminal one. I very much doubt the police will be interested in pursuing anything. In general terms, the legal recourse would be to sue the editor in the civil courts. I suspect that the costs of doing so outweigh the benefits.

Could you report it to the editor's university? Yes. However, it isn't clear what this would achieve. As @ZeroTheHero says, they (apparently) have no involvement in the dispute so far. From their perspective it will be your word against the editor's; even if they wanted to resolve the dispute, it is not clear how they would go about doing so.