No. The person the grievance is about shouldn't investigate or hear it. You need someone independent and impartial, which is a real headache in a small business.
If you honestly have no one suitable in-house, that's a common reason owners bring in an outside person to hear the grievance or run the investigation, so it can't be picked apart later as biased.
Every situation has its own details, and those details change the right answer. For a read on yours, take the free Employee Situation Check or book a call.
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How to handle this, in a couple of minutes
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General guidance to help you decide your next step, not legal advice. Employment law changes, so always check the current position for your own situation.