The CSS

Just like with downloading the Javascript, you can do with the CSS.

https://raw.githubusercontent.com/peterbe/autocompeter/master/public/dist/autocompeter.min.css

Or...

bower install autocompeter
ls bower_components/autocompeter/public/dist/*.css

Or...

<link rel="stylesheet" href="//cdn.jsdelivr.net/autocompeter/1/autocompeter.min.css">

There is also another alternative. If you already use Sass (aka. SCSS) you can download autocompeter.scss instead and incorporate that into your own build system.

Overriding

It's very possible that on your site, the CSS doesn't fit in perfectly. Either you don't exactly like the way it looks or it just doesn't work as expected. The recommended way to deal with this is to override certain selectors. For example it might look like this:

<link rel="stylesheet" href="//cdn.jsdelivr.net/autocompeter/1/autocompeter.min.css">
<style>
._ac-wrap { width: 400px; }
@media only screen and (max-width : 321px) {
  ._ac-wrap { width: 290px; }
}
</style>

As an example, with the design being used on autocompeter.com some CSS had to be overridden.

About using a CDN for CSS

Note, if performance is important to you, note that it's actually not a good idea to use the CDN URL to reference the stylesheet. The reason for that is that oftentimes, a DNS lookup is actually slower than CSS download from a lesser fast server.

There's a lot of resources online, like this one, that elaborate this in much more detail.