To fly a helicopter you must have a current license and a current medical certificate on your person.
As far as contact with ATC you may or may not need to be in contact with them. It depends on where you are flying. Different airspace has different requirements in order to keep your license you must abide by their (The FAA’s) rules. When I fly I normally do not contact ATC but that is only due to where I fly. So, the short answer in my case is no.
There are of course many other requirements, weather, inspections, maintenance, pilot recency and qualifications but that is a whole other topic.