Can a dude move independently without an action? I mean can a dude move somewhere without an action token.
Under PLAYING THE GAME in the rule book...
Place action tokens on your town card to show where your dudes will move and what actions they will take this round. Place a token face down if you do not want your dude to take any actions.
Therefore, to indicate that a dude is not taking an action, you use a face down action token, but you must still place the token. Honestly, I would recommend placing an action for the dude even if you do not plan on taking that action (since you are not forced to take that action - see ACTIONS). It leaves more options open for you.