Being lawyers, we usually have a quick answer to this: legal counsel. We recognize, however, that clients don’t have unlimited funds. So practically speaking, each situation will have to be assessed on its own facts.
In situations where a simple fact finding determination and assessment of credibility are all that is needed, the skilled manager can suffice, with counsel in the background to point them in the right direction and give legal advice based on any facts that are gathered.
In other situations, such as where the employer wishes to demonstrate it retained a skilled expert to address a serious workplace problem (i.e. a case of sexual harassment or alleged systemic racism in the workplace) a lawyer with expertise in this area is desirable.
Sometimes a client would like to maintain privilege over an investigative process and report. If the incident is so serious that your organization risks serious liability depending on the outcome, you may wish for a lawyer to investigate for the purpose of providing legal advice and assessing liability, as well as giving recommendations based on that legal advice.
Provided the process, including any terms of reference, make it clear that the purpose of the investigation is to give legal advice, the entire investigative report may be privileged from disclosure in subsequent legal proceedings.
In short, while a lawyer will cause additional expense, in very serious situations, or in situations where you do not have the internal capacity to conduct the investigation, legal counsel or, at the very least, a qualified external investigator should be considered.