Copying taxonomy term to custom field

Try hooking into ‘save_post’ action:

add_action( 'save_post', 'your_state_term_save' );

function your_state_term_save( $post_id ){

    // Bail if we're doing an auto save
    if( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) return;

    //check if they selected your state term
    $state = isset($_POST['tax_input_field_name']) ? $_POST['tax_input_field_name'] : ''; //make sure of what the input name is here...

    //insert post meta
    update_post_meta($post_id,'state',$state);
}

This works by waiting till the post is saved and grabbing the taxonomy term right out of the $_POST vairable.