Doesn't matter if the Police Detective thinks a crime has taken place. He has to screen it with the local prosecutor's office and their bar is much higher than thinking a crime has taken place. They pretty much have to be convinced that they can get either a guilty plea(not likely in this case) or be able to prove beyond a reasonable doubt that a crime took place.

I have no idea why it is taking so long to decide on prosecution in this case. When you boil it down it is a pretty simple battery case. The only part that really matters is what led up to whatever happened, the event itself and the immediate aftermath. Did he assault her or not? If you can't prove it in 3 months in screening you probably can't prove it beyond a reasonable doubt in front of a jury either.

If they do decide to prosecute they are in for an expensive deal for a case that would (locally anyway) be nothing more than a misdemeanor battery case.