How do I conditionally enqueue script for CPT single post type with plugin?

Make sure your code runs in wp_enqueue_scripts action hook.

Also checkout your script handle 'owl.carousel.js'. In wp_script_is(), it is not the same than in the 2 later functions in which you enter it as 'owl.carousel.min.js'.

add_action( 'wp_enqueue_scripts', 'enqueue_properties_scripts' );

function enqueue_properties_scripts() {
    if ( 'properties' === get_post_type() ) {
        if ( wp_script_is( 'owl.carousel.min.js', 'enqueued' ) ) {
            return;

        } else {
            wp_register_script( 'owl.carousel.min.js', plugin_dir_url( __FILE__ ) . 'js/owl.carousel.min.js' );
            wp_enqueue_script( 'owl.carousel.min.js' );
        }
    }
}