I know this is possible, and I have seen it done, I just do not know how to do it myself, or where to find documentation.
I want it so the user can enter text in a textfield, and then push a button, and it opens the official Twitter for Android app, and puts the text entered in the textfield, into the status update on the Twitter app.
If you are wondering where I have seen this done, it is with the CNN app (and other news apps), where you click share, you can choose twitter and it puts the link and headline as a status update.
It uses an Intent to launch the Twitter Android app: take a look at http://lisudza.wordpress.com/2010/12/29/tweeting-using-twitter-for-android-intent/ and see if it covers what you want.