There is a process that occurs at discharge from the hospital, you can’t just get up and leave.
There will be paperwork that needs to be filled out and signed prior to going home.
Many hospitals require a car seat and some will even check to see that it is installed correctly.
You will need a discharge order from both your obstetrician and your baby’s doctor prior to leaving the hospital. There will be follow up instructions for you and your baby as well as instructions for home.