How to share data between self-hosted Web API and server

Question

I have created a simple self-hosted web api and a server that is basically a windows service.

Service has the following code:

protected override void OnStart(string[] args)
        {
            var config = new HttpSelfHostConfiguration("http://localhost:8085");

            config.Routes.MapHttpRoute(
               name: "API",
               routeTemplate: "{controller}/{action}/{id}",
               defaults: new { id = RouteParameter.Optional }
           );

            HttpSelfHostServer server = new HttpSelfHostServer(config);
            server.OpenAsync().Wait();
        }

Web API

 public class ValuesController : ApiController
    {
        public String GetString(Int32 id)
        {
            return "Test data";
        }
    }

Is there a way to do object sharing between the service and the web api? For example, connect to a database server in the service and use the connection object in web api etc.

Basically for this problem, I don't have any idea if this is possible and how. I searched on the internet but unable to reach the desired location.