Which is correct usage?
- complaint dated 01.02.2013 by a customer
- complaint dated 01.02.2013 of a customer
Both are correct, though the second is ambiguous, and there's a reason to favour yet another.
The customer made a complaint. It is not necessarily to you, though that would be guessed from context. It might be favoured if you were talking of a complaint made to a consumer association rather than to you.
Could mean the customer made a complaint, or could mean someone complained that there was a customer. At as stretch it could mean a complaint about a customer. It would be clear which meaning you meant, but the other possibilities can make it jar slightly.
The same as "by a customer", but with a stronger focus on the receiving of the complaint. While it could be used of a complaint made to another body (again, e.g. a consumer association), unless this was made clear, it would be understood as a complaint you yourself received.
So, if the records are of complaints directly received, favour from. If you are including both direct and indirect complaints, favour by.
complaint dated 01.02.2013 by a customer
complaint dated 01.02.2013 of a customer
complaint dated 01.02.2013 from a customer
But 'complaint dated 01.02.2013 of a customer' would imply that the customer is the subject of the complaint.