What happens if you take a shortcut and hire the first painting company that you find and discover that it doesn't have insurance coverage? Hopefully, nothing goes wrong, and then you won't have any legal issues.
Unfortunately, if you hire painters and they aren't covered by insurance, you are responsible for anything that happens while they are working at your home. This includes injuries to a person and damage to the environment. The best way to avoid the potential for legal problems is to hire a reputable painting company covered by insurance rather than an unsafe one that doesn't have any coverage at all.
You can be held responsible for negligent behavior, such as paint spills, in which case, the EPA (Environmental Protection Agency) might become involved. If any contamination occurs, you are probably going to become legally and financially responsible, something you can easily avoid by hiring a reputable painting company.
Likewise, if anything happens to them while they are working on your project, you are liable if for it. Hiring someone from a painting company that doesn't have workmen's compensation insurance is the same as hiring the workers as your employees, making you the responsible party in the event of an injury.