Yes, you can do it without any third-party library. See my IronPython sample posted on the IronPython Cookbook site that shows you exactly how. Even if you don't program in IronPython, the main part of the code that should get you started is repeated below and easy to port to C#:
ServicePointManager.Expect100Continue = False
wc = WebClient(Credentials = NetworkCredential(username, password))
wc.Headers.Add('X-Twitter-Client', 'Pweeter')
form = NameValueCollection()
form.Add('status', status)
wc.UploadValues('http://twitter.com/statuses/update.xml', form)
Basically, this does an HTTP POST to http://twitter.com/statuses/update.xml with a single HTML FORM field called status
and which contains the status update text for the account identified by username
(and password
).