Format on homepage only

I am trying to format the td-header on home page only, but no success so far.
This code works but applies to all sites;

tc-header {
background: rgba(0, 0, 0, 0.3);
height: 48px;
background-image: none;
position: fixed;
}

Homesite has class home, this works;

body.home {
background: black;

How can I css td-header only on homepage?

}