It depends. Claims of unlawful conduct like sexual harassment or race discrimination are said to require an investigation. That is because EEO policies encourage employee complaints of that nature and state than an investigation will occur in response. Courts view investigations as the employer’s exercise of reasonable care in response to such concerns.
I recommend a two-part analytic to determine if an investigation is indicated that encompasses both legal claims as well as potential legal issues. First, is there suspected or alleged misconduct that if substantiated would prompt some level of disciplinary action? If so, are relevant facts or perceptions involved in conflict? When the answer to both questions is “yes,” an investigation is necessary to resolve the issue.
Sometimes the process of investigation is valuable even absent underlying conflict to allow affected individuals the opportunity to tell their stories.