Sample script runs a Selenium test, captures the session ID and updates the session status on BrowserStack

Program.cs

using System;
using OpenQA.Selenium;
using OpenQA.Selenium.Remote;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Reflection;
using System.Threading.Tasks;
using System.Net;
using System.IO;

namespace SeleniumClientTry
{
	public class CustomRemoteWebDriver : RemoteWebDriver
	{
		public CustomRemoteWebDriver(Uri remoteAddress, ICapabilities desiredCapabilities) : base(remoteAddress, desiredCapabilities)
		{
		}

		public string getSessionID()
		{
			return base.SessionId.ToString();
		}
	}

	class Program
	{
		static void Main(string[] args)
		{
			CustomRemoteWebDriver driver;
			DesiredCapabilities capability = DesiredCapabilities.InternetExplorer();
			capability.SetCapability("browserstack.user", "<USERNAME>");
			capability.SetCapability("browserstack.key", "<ACCESS_KEY>");
			capability.SetCapability("browserName", "internet explorer");

			driver = new CustomRemoteWebDriver(
			  new Uri("http://hub.browserstack.com/wd/hub/"), capability
			);
			driver.Navigate().GoToUrl("http://www.google.com");
			Console.WriteLine(driver.Title);

			IWebElement query = driver.FindElement(By.Name("q"));
			query.SendKeys("Browserstack");
			query.Submit();
			Console.WriteLine(driver.Title);

			//Works without using the subclass for client-side bindings <= 2.48.2
			//var sessionIdProperty = typeof(RemoteWebDriver).GetProperty("SessionId", BindingFlags.Instance | BindingFlags.NonPublic);
			//SessionId sessionId = sessionIdProperty.GetValue(driver, null) as SessionId;
			string sessionId = driver.getSessionID();
			Console.WriteLine(sessionId.ToString());

			System.Threading.Thread.Sleep(10);

			var url = string.Format("https://www.browserstack.com/automate/sessions/{0}.json", sessionId);
			Uri myUri = new Uri(url);
			WebRequest myWebRequest = HttpWebRequest.Create(myUri);
			HttpWebRequest myHttpWebRequest = (HttpWebRequest)myWebRequest;
			NetworkCredential myNetworkCredential = new NetworkCredential("USERNAME", "ACCESS_KEY");
			CredentialCache myCredentialCache = new CredentialCache();

			myCredentialCache.Add(myUri, "Basic", myNetworkCredential);
			myHttpWebRequest.PreAuthenticate = true;
			myHttpWebRequest.Credentials = myCredentialCache;

			WebResponse myWebResponse = myWebRequest.GetResponse();
			Stream responseStream = myWebResponse.GetResponseStream();
			StreamReader myStreamReader = new StreamReader(responseStream, Encoding.Default);

			string pageContent = myStreamReader.ReadToEnd();
			Console.Write(pageContent);
			responseStream.Close();

			myWebResponse.Close();
			System.Threading.Thread.Sleep(10);

			driver.Quit();

			System.Threading.Thread.Sleep(3);

			string reqString = "{\"status\":\"Failed\", \"reason\":\"There was a Error!\"}";

			byte[] requestData = Encoding.UTF8.GetBytes(reqString);
			Uri myUri1 = new Uri(string.Format("https://www.browserstack.com/automate/sessions/"+sessionId+".json"));
			WebRequest myWebRequest1 = HttpWebRequest.Create(myUri1);
			HttpWebRequest myHttpWebRequest1 = (HttpWebRequest)myWebRequest1;
			myWebRequest1.ContentType = "application/json";
			myWebRequest1.Method = "PUT";
			myWebRequest1.ContentLength = requestData.Length;
			using (Stream st = myWebRequest1.GetRequestStream()) st.Write(requestData, 0, requestData.Length);

			NetworkCredential myNetworkCredential1 = new NetworkCredential("USERNAME", "ACCESS_KEY");
			CredentialCache myCredentialCache1 = new CredentialCache();
			myCredentialCache1.Add(myUri, "Basic", myNetworkCredential1);
			myHttpWebRequest1.PreAuthenticate = true;
			myHttpWebRequest1.Credentials = myCredentialCache;

			myWebRequest1.GetResponse().Close();
		}
	}
}