This is how to make PUTs and POSTs:

def requestMethod = "PUT";
def URLParam = []
def baseURL = "http://myserver.domain.dk/"


def url = new java.net.URL(baseURL);
URLConnection connection = url.openConnection();
connection.setRequestMethod(requestMethod);
connection.doOutput = true
connection.setUseCaches(false);
connection.setRequestProperty("Content-Type", "text/html");
connection.setRequestProperty('Authorization', 'Basic ' + 'username:password'.bytes.encodeBase64().toString());

//PUT Content
OutputStreamWriter out = new OutputStreamWriter(
    connection.getOutputStream());
    out.write("type=0");
    out.write("&format=0");
    out.write("&content_id=" + ListId);
    out.write("&jira_key=" + IssueKey);
    //out.write("options={\"status\":\"" + issueStatus + "\"}");
    out.close();

//try
//{
  log.info "Script=MakeReport.groovy IssueKey=" + IssueKey + " ScriptRunIdent=" + scriptRunIdent + " URL=" + baseURL
  log.info "Script=MakeReport.groovy IssueKey=" + IssueKey + " ScriptRunIdent=" + scriptRunIdent + " Action=GetHttpsConnection"
  connection.connect();
  try
  {
    connection.getContent()
  }
  catch (Exception ex)
  {
    log.info "Script=MakeReport.groovy IssueKey=" + IssueKey + " ScriptRunIdent=" + scriptRunIdent + " Error=ConnectionError Message="+ ex.getMessage()
  }
  String Status=connection.getResponseCode()
  String Message=connection.getResponseMessage()