For the most part, the investigation in a DV is done by the officer on the scene. Very few agencies (out here anyway) have a detective doing much follow-up on these matters, and when they do, the suspect has already likely been arrested or is pending an arrest.
Of course, much of the time in a DV if the suspect does NOT say anything, then you have ONE account of the incident (the victim's) and this is usually sufficient to incriminate the suspect and establish the probable cause for an arrest. However, had the defendant made a statement, he may not have gone to jail at all as it can often turn the entire tale around or render the determination of the primary abuser more difficult or require it to go to the DA, instead. I have seen many instances where the suspect's refusal to say anything resulted in him being arrested and charged when his statement would have clarified matters and resulted in his NOT being arrested and maybe even being the victim. Though, if he DID thump her, it might be best to shut up and take you proverbial lumps.
Two days ago I was at a call where the victim accused estranged hubby of thumping her and had he been silent and not told his side of the story, he would have gone to jail. As it was, his story provided additional questions to provide to the victim and we were able to determine that her story was not entirely accurate and that there was insufficient probable cause to make an arrest against either of them for the incident and we had to send it to the DA for a decision. Had he remained silent he would have been arrested and booked.
So, it all depends ...