Almost all of us have been in your shoes or very similar ones. I, too, am wondering your child's age. With a diagnosis of Conduct Disorder, this implies teenage years, not yet adulthood. If he is still in high school, the school district is legally obligated to help you find and pay for residential treatment if your child is on an IEP. From what you write, your son should qualify for Special Education with an IEP, if he doesn't already have one. My son was always in special education with an IEP based on ADHD alone. Depression is also qualifying. The school districts can be difficult when disorders of conduct disorders are involved. With depressed teen males, disordered conduct is very frequently part of depression. I worked in schools and sat on IEP committees. Please keep posting. You will find support here.
The very first thing to do is request an immediate emergency IEP in writing. You should be able to find a community member to help as an advocate. Eventually, I was able to find a free attorney from a Special Education Rights and Advocacy program, but that was because I was living near a big city.