I'm going crazy here. I thought I had a handle on Polymer styling, but alas.
I've got:
<my-app>
  <sign-in>
    <core-overlay>
In sign_in.css I style:
core-overlay {
  background: red;
}
But it doesn't work!
My sign_in.html is:
<link rel="import" href="../../../../../../../packages/polymer/polymer.html">
<link rel="import" href="../../../../../../../packages/core_elements/core_overlay.html">
<polymer-element name="sign-in">
  <template>
    <link rel="stylesheet" href="sign_in.css">
    <core-overlay id="overlay" class="overlay" layered backdrop opened="false" transition="core-transition-center">
      <span id="message">Please sign in to comment.</span>
      <button class="signin-btn" id="facebook-signin" on-click="{{signInWithFacebook}}">Sign in with Facebook</button>
    </core-overlay>
  </template>
  <script type="application/dart" src="sign_in.dart"></script>
</polymer-element>
 
                        
The backdrop and core-overlay elements are created dynamically as child of
<body>. To style it you add the following css to your entry page CSSbackdrop
overlay
The overlay css is copied from https://github.com/Polymer/core-overlay/blob/master/demo.html#L38-L49.
The core-overlay demo uses a custom Polymer element
x-dialogto encapsulate the core-overlay and the CSS.