Potions of paralysis may be thrown at monsters for an effect of 1-25 turns. Monsters may also throw it at you for weakened effect (1-5+ turns). The BUC status of the potion has no effect when using it against a monster. Using the potion on an already paralyzed monster ends any current paralysis and then paralyzes the monster for 1-25 turns. Using the potion on a monster that does not move has no effect.
If you are wearing a ring of free action, you should preferably wield it so it will hit. For example, most quest nemeses will pick up the quest artifact as soon as they are awake and become magic resistant. Paralysis gives you some time to magic missile them.