You sign two forms, therefore authorize two organizations, to share your information with HPD. A Medical information Waiver for your personal healthcare provider, and a Mental Health waiver for the state Adult Mental Health Division. Those are the only two places that will be contacted.
For the medical information form, if you have an HMO, chances are no doctor will ever look at it. Some clerk will complete the form based on information in your record. If you have never seen anyone for counseling or mental health. you should be good.
If you have a local doctor outside of a large HMO, hospital or clinic, then you should probably give the provider a heads-up that they may see the form from HPD soon. Never hurts to bring the subject up since he/she will be asked about your fitness to own guns.
The process is designed to be hands-off for you. You sign the waiver, HPD sends it to your provider, and the provider replies. If the provider fails to reply, your application should still be approved.