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I would like to share minimum three way of writing such letter:-
1. We are investigating your allegations and you'll hear from us shortly.
2. We are initiating an immediate investigation of the incident you reported to us and wish to apologize in advance for any inconvenience if occurred.
3. We regret any difficulties you may have encountered recently with our staff. we'll investigate the matter promptly and contact you shortly with our findings.
As Mr. Divyesh said third point sounds better than the other two letters. is it not?.
If the complaint was in the form a letter, Request him for an appointment at his premises to fix a convenient timing for the meeting by a competent official. In between make an apology of the incident, and inform him the initiation taken by the company for a detailed investigation assuring necessary action from the company side in the most appropriate way.
You start of by apologizing on behalf of the rude colleague.
