You are free to apply of course. But chances are that the opening isn't available (HR doing some ground testing) or they have not found a suitable candidate (that means you included). With that in mind, reapplying will not increase your chances for the same opening. Suggest you look for other openings instead.

Word of advice, all public agencies are experiencing a headcount freeze. Every new hire must be strongly recommended to justify hiring them. Expect the entry barrier into public agencies to be higher than before.