There is Rc and Arc, the latter being atomic. If you want to pass them between threads, you'll want an Arc, and in fact you will want an Arc<Mutex<Data>> so your data becomes:

  let data = Arc::new(Mutex::new(Data::new()));

And if you want a mutable static global that's accessed across threads, you'll need something like:

  lazy_static! {
    // 0 -> None
    // 1 -> Circles
    // 2 -> Bezier
    static ref DRAW_ON_TOUCH: Arc<Mutex<u32>> = Arc::new(Mutex::new(0));
  }

I love Rust but it is making easy things harder than they need to be.