I refer to your complaint letter which was received on date.
I would say
I am writing in response to your complaint which we received on...

Student or Learner
Hello there. I always tried to send a decent interim reply letter to our complainants before any thorough action is to be taken. Here is my draft one:
I refer to your complaint letter which was received on date.
The matters reported in your complaint letter regarding the above company are now under investigation and I shall inform you of the result as soon as possible.
Any comments on that?
Cheers.
I refer to your complaint letter which was received on date.
I would say
I am writing in response to your complaint which we received on...
When people call with a problem, it means a lot if you show that you care and will be responsible enough to follow up. May I suggest:
Dear [Jane Doe]:
In response to your letter to me dated January 1, 2006, I am concerned to learn of your dissatisfaction with regard to [explain briefly the nature of the complaint]. I have placed a call with [individual who is responsible] to investigate this issue. Once I have reviewed the details surrounding this problem, I will contact you by [telephone] so that an amicable resolution can be achieved.
In the meantime, do not hesitate to contact me directly.
Sincerely,