If a hysteroscope d&c is done in the hospital, is general or local anesthesia given?

Depends: what is diagnosis and goals? General or spinal could be offered. Local less likely!

Often general: general anesthesia or quite a heavy sedation is commonly used, that can be supplemented by local anesthetic from gynecologist; ultimately though it is discussion with your anesthesiologist that should help to chose the safest and most comfortable anesthesia plan for you.

Yes to either.: Depending on the training and skills of your surgeon the anesthetic can be a full general of local block only by surgeon or combination of local block w sedation by anesthesia provider.

GYN ANESTHESIA: The majority of these procedures are done with the patient under general anesthesia. However, it is perfectly reasonable to have this procedure done with moderate sedation (MAC-Monitored Anesthesia Care) administered by the Anesthesiologist, in combination with a local anesthetic placed in the paracervical region by the Gynecologist.

General: To most patients, general anesthesia means being "asleep" or unaware of what is happening compared to a procedure done under local anesthetic (awake). For a D&C, you will either have general anesthesia or a version of twilight/sedation anesthesia.