Holding a class instance in a Static object in C#

We have a class "DataAccessServiceConnector", in which we have few methods to communicate with Data Access Service.

public class DataAccessServiceConnector: IDataAccessServiceConnector
{
     public async Task<HttpResponseMessage> GetDataAccessServiceResponse()
     {
        //Some code
        return GetDataFromDataAccessService();
     }        
}

We have an Interface:

public interface IDataAccessServiceConnector
{
    Task<HttpResponseMessage> GetDataAccessServiceResponse();
}

And having a different class, that is holding the instance of "DataAccessServiceConnector" class in the as static object.

public class ClassA
{
  public static IDataAccessConnector DataAccessConnector;
  //Constructor of the Class
  ClassA()
  {
     DataAccessConnector = DataAccessConnector ?? new DataAccessConnector();
  }
}

Is it bad practice to hold the class instance (i.e. DataAccessServiceConnector) in a static object(i.e. DataAccessConnector)?