Hi there @paramathesh
By default, State and Country fields should be required in WooCommerce core. I am running version 3.4.3 on my test site, and these fields are required (with only WooCommerce active). It sounds like there may be something interfering with this default behaviour.
This kind of problem is usually caused by either a conflict with your theme or with another plugin.
The best way to determine if the issue is being caused by a theme and/or plugin is to temporarily switch your theme to Storefront and disable all plugins except for WooCommerce. If you can install plugins, install Health Check. On the troubleshooting tab, you can click the button to disable all plugins and change the theme for you while you’re logged in to that session without affecting normal visitors to your site. Note that Health Check may not count Storefront as a default theme, so you can also use Twenty Seventeen as well.
If that resolves the issue, then one-by-one you can switch back your theme and re-enable your plugins, testing in between, until you find the one causing the conflict.