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From following various murder cases, my initial thought is: how long is a piece of string?
I've seen arrests happen within weeks and I've seen arrests happen 3 years out. Average is maybe 4 to 6 months. It all depends on if a body is found, what evidence exists, what that evidence can prove, and how comfortable a DA is in taking a case for indictment.
In my area a previous DA was very conservative and would not agree to prosecute a case until he was comfortable he could prove the charges and he would wait as long as it took, even if that took years, because if there's not enough evidence and a jury aquitts, that's it, no second chances.
In one famous and horrific case in my local area, Michelle Fisher Young was found murdered at home, the murder occurred in 2006 and the arrest for her murder didn't occur until 3 years and 1 month later. Her husband committed the murder and is in prison for life.