In some cases, yes. However, while the law may require you to investigate, it can be vague on the size and scope of that investigation. As an employer, you are required to do your due diligence in investigating before taking action. For a single isolated incident where an employee makes an off-handed comment and then quickly apologizes for their actions, a full-scale investigation will likely not be required.
However, employers should be cautious about writing off an incident as small or isolated before investigating further. A single complaint might cast light on a much longer pattern of problematic behavior from an employee. One incident of theft caught by another employee may reveal that there has been a past history of incidents that had previously gone unnoticed. Not every situation will require an external third-party investigator, but employers should always do their due diligence before dismissing any incident outright.
If you believe that an employee has engaged in serious misconduct that could lead to dismissal for cause, it is critical that you investigate first. Courts are inclined to penalize employers who do not provide an employee with some form of “due process”, which includes a chance to respond to allegations or concerns. Employers who fire first and ask questions later often end up paying not only wrongful dismissal damages, but damages for proceeding in bad faith.