You may be apart of a smaller organization and have no funds for outside resources. You may be apart of a medium to large company that has a highly skilled HR Investigator that has received specialized workplace investigation training. You may have always handled complaints & investigations improperly or never had a serious workplace investigation so you have no clue what to do.
An outside investigator would be my preference. Our firm (HR Learning Center) handles workplace investigations quite often because our client companies don't want a partiality claim filed against them. An outside investigator or outside legal counsel should have no personal interests or ties to the company. There are increased risks when HR personnel is involved in workplace investigations. You would not want a complaint of bias due to someone in HR that may be partial to the accused or complainant in the case.
Sally (HR Manager) may be friends with Judy (complainant) and also dated Steve (accused) for 5 months while in grad school in 2005. Sally may now hate Steve, warned Judy not become too close to Steve and now she is handling this investigation. What a coincidence! Who knew that Sally and Steve even attended the same grad school? That sounds like a recipe for disaster. Sally doesn't have to know or have known Steve or Judy prior to this situation. Sally could simply be more friendlier with Judy than Steve. Sally could have worked with Judy longer. Sally could have played on the company's softball team with one of Steve's daughters. Sally could know that Steve regularly goes to church and feels he is not capable of the accusations filed against him. Guess what? None of those reasons matter. But all of those are exactly why workplace investigations are plagued with the constant risk of bias and partiality complaints.
Bottom line, you don't want a claim of partiality and you want a thorough and effective investigation conducted.