Hi Willie,
I am not much of a .net programmer, but I do have a Java example. You might be able to deduce how to do it from that?
System.out.println("Creating Test Case Result...");
JsonObject newTestCaseResult = new JsonObject();
newTestCaseResult.addProperty("TestCase","/testcase/99999999999");
newTestCaseResult.addProperty("Workspace","999999999999");
newTestCaseResult.addProperty("Project","999999999999");
newTestCaseResult.addProperty("Build","9");
newTestCaseResult.addProperty("Verdict", "Pass");
newTestCaseResult.addProperty("Date","2016-05-09T16:14:00");
newTestCaseResult.addProperty("Notes", "Blah");
newTestCaseResult.addProperty("Tester", "/user/9999999999");
CreateRequest createRequest = new CreateRequest("testcaseresult", newTestCaseResult);
CreateResponse createResponse = restApi.create(createRequest);
You can use the online interactive WSAPI document to determine which attributes are required for TestCaseResult.
https://rally1.rallydev.com/slm/doc/webservice/
Let me know if that helps or not.
Thanks,
Sean Davis