ASP.NET WEB API do i need async client

I have a Web API application which exposes certain async methods, such as:

public async Task<HttpResponseMessage> Put(string id){
  var data = await Request.Content.ReadAsStringAsync();
  //do something to put data in db

return Request.CreateResponse(HttpStatusCode.Ok);
}

I also have a class library that consumes this API with System.Net.WebRequest like this:

   var request = (HttpWebRequest)WebRequest.Create(url);
   var response = await request.GetResponseAsync();

Does the response need to be retrievend async? If so, why? Or can I also use request.GetResponse();.

I used the GetResponse before which would sometimes throw a 500 error ( An asynchronous module or handler completed while an asynchronous operation was still pending). Once I changed it to GetResponseAsync(), I stopped receiving this error.

EDIT: Code that sometimes throws a 500 error

I had the web api method stripped down to (just to check whether the 500 error was business logic or something else). Note: this is after changing the consumer to async (first function is the consumer, then the api method):

    public HttpWebResponse(GetApiResponseForPut(string url, string putData, NameValueCollection headers)
    {
      var request = (HttpWebRequest)WebRequest.Create(url);

            request.CookieContainer = _cookieContainer;
            request.Method = "PUT";

            if (headers != null)
            {
                request.Headers.Add(headers);
            }

            var encoding = new ASCIIEncoding();
            var byte1 = new byte[0];
            if (putData != null)
            {
                byte1 = encoding.GetBytes(putData);
            }

            request.ContentType = "application/x-www-form-urlencoded";
            request.ContentLength = byte1.Length;



            Stream requestStream = request.GetRequestStream();
            requestStream.Write(byte1, 0, byte1.Length);

            requestStream.Close();
            var response = await request.GetResponseAsync();
            return (HttpWebResponse)response;

    }

    public async Task<HttpResponseMessage> Put(string id)
    {
      HttpResponseMessage response = Request.CreateResponse(HttpStatusCode.OK);
      return response;
    }