Keep in mind, there are three basic forms of hospital employment (or quasi-employment).
1. Attending physician privileges - the doctor (MD, DO, DDS/DMD-OMFS, or DPM) has staff privileges to use the OR, ER, visit patients, write orders, etc., but is not an employee of the hospital. He/she has a special contractual relationship with the hospital, but is not employed by the hospital. Liability flows back to the physician, but can be shared by the hospital if nurses and hospital employees are involved. These privileges are obtained through application to the hospital credentialing committee and are granted to licensed MDs, DOs, oral-max facial surgeons (dentists with additional training), and podiatrists. Rarely, PhD/PsyD psychologists are granted privis to attend to psychiatric patients only. Some NPs have privileges too. There is no pay involved. In fact, in come situations, but not all, the doc pays a few to use the hospital and be on staff. Privis include admit and d/c authority, lab requests, patient orders (labs, x-rays, MRIs, PETs, etc.), etc.
2. Staff Employment - A professional or non-professional employee of the hospital. The hospital hires the employee and he/she is classified as a pharmacist, phlebotomist, tech, respiratory tech, x-ray tech, RN, LPN, optometrist, PT, etc. The hospital has full liability for an employee, unless the employee acts in a criminal manner (assault, battery, criminal sexual conduct, rape, drug offenses, etc.) or a grossly negligent manner. There are many hospitals who hire ODs as employees for vision clinics, vision research centers, pre-surgical screening centers, etc.
3. Contractual relationships - an OD can also be hired as a special consultant or advisor to a hospital board, committee, or center for a limited purpose.
So, if you're interested in working as an optometrist in a hospital setting, you may find work as an employee, but you'll likely never find work as an attending physician or optometrist with hospital privileges.