Can the non-custodial parent refuse a certified letter from the custodial parent?
Unless it is from a court or law enforcement, you are under no obligation to adopt it.
But, if there are negative consequences, you have no defense....you can't voice you weren't notified.
You can refuse anything you want. Hell, you can accept it, and never read it. However, if this become mention in a court of law in evidence of correspondence, and your deficiency of cooperation, then you could see consequence.