Good practices with Dapper

I'm a Beginner with Dapper and I have some doubts about best practices. My project is a Asp.net WebApi.

Opening Connection String

In this thread the connection with the database is opened like this,inside of Controller, but it is a simple project, not meant to be a WebService :

static IDbConnection db = new SqlConnection(ConfigurationManager.ConnectionStrings["SqlServerConnString"].ConnectionString);  

But I found other examples with using statement :

using (IDbConnection connection = new SqlConnection(stringConnection))
{
    //do something
}

Since this project is a WebApi the using statement would be better cu'z it would Dispose the request ?

Listing Data

In the same thread above shows how to retrieve a list based on static IDbConnection db property :

var res = (List<ShippDetails>)db.Query<ShippDetails>(query, new { id });

Or would be better to use .AsList() ?

var res = connection.Query<ShippDetails>(query, new { id }).AsList();

The Action of the Controller

For all my Action it goes like :

[Route("FF")]
    [HttpGet]
    public async Task<HttpResponseMessage> get()
    {         
        var response = new HttpResponseMessage();
        int id = 1;

        var res = (List<ShippDetails>)db.Query<ShippDetails>(query, new { id });

        if (res.Count > 0)
        {
            response = Request.CreateResponse(HttpStatusCode.OK, res);
        }
        else
        {
            response = Request.CreateResponse(HttpStatusCode.NoContent);
        }          

        var task = new TaskCompletionSource<HttpResponseMessage>();
        task.SetResult(response);
        return await task.Task;
    }

It could cause some kinda of Delay? Or the way I'm handling my Action is "Good"? Thanks!