Don't say "on the other hand" if you haven't used "on the one hand..." first. You need the two parts together to make the thing complete:
She's crazy. On the other hand, she's a good worker.
You use "on the one hand/on the other hand" to compare and contrast two things that are logically connected:
- On the one hand, she's a good worker. On the other hand, her work is often late because her time management skills aren't very good.