Glad that was accessible to you. When I was divorced many years ago we had no health insurance; I took the kids to the county health department for their immunizations. Maybe it was because it was a county rather than state HD, but the only other things they provided there were vision and hearing screens and head lice checks/medicated shampoo. When the girls were older I took them to PP for their well-woman checks.
We lived in Missouri then; I remain unaware of any state-run health department other than the governmental one that looks out for public health safety but doesn't provide any direct patient care.
Every county in the entire U.S. has a county-run State Health Dept. Some have multiple locations in the same county, especially the larger ones. They can even get people signed up for free transportation for the poor who live out in the more rural areas with no cars. I worked in the accounting dept. of the Marion County HD in the Child Health building. I sat at that check-out window 5 days a week, gathering insurance information, taking payments, entering demographic info for new patients and billing insurance, Medicaid & Medicare. So, I got to see first hand the prices of what the taxpayers were paying for all those "free" births of babies at hospitals (at that time it was $1200.00 a pop), all the "free" pre-natal care, medicine, counseling, WIC, well-baby care, labs, sonograms, family planning services, condom, birth control pills, depo shots, etc.........FREE!
The sad and maddening thing was even they were determined to be on a sliding fee scale for like $5 or $10 a visit, all they had to do was tell me at the window they didn't WANT to pay (not they weren't ABLE to pay) and I had to just let them walk. It's a pretty sick set-up but, we all had to just keep our mouths shut to keep the gravy train rolling to those at the top there.

Our hearts would break for the few truly destitute and homeless...the rest.........just gamers.
In between the exiting patients I would sit and work on past billings and accounts that needed to be caught up on to try and keep us current within a 1 month time frame. We were paid by State of Florida. In 2011 (or 12?) we had massive State layoffs which I knew would eventually happen even from my 1st day on the job. So, I just took the job anyway because it was offered and it was eye-opening to see what goes on behind the scenes. There was corruption right up to the top with the Director. I found out a couple years after I left that quite a few of old top people were caught in some "stuff" and were fired. Can't beat Karma, LOL. There's no way for a socialist system to work forever, you run out of money due to abuse and gaming of the system.
I will never, EVER forget the times I would hear children at the window talking to their moms saying things like, "Mom can we go to IHOP now???" Of the moms would always say something like, "Sure baby, just a minute".
I always had to excuse myself and go outside for break and scream and shake my head. I brown-bagged my lunch EVERY single day and these people with all their free stuff are dining out. Gimme a break.
"The problem with socialism is that eventually you run out of other peoples' money." ~ Margaret Thatcher