Is there any restrictions on a part time teller working at two different banks?

The only restrictions would be found in your employee handbook and conflict of interest policy. Back in the day, outside employee was not allowed, but that has loosened over the years. I would find it pretty unusual though for a policy that would allow an employee to also work for a direct competitor, not to mentioned the heightened risk of a teller working in two different banks which allows them to process transactions at both locations. Typically all outside employment must be disclosed and approved. If your policies do not address this, they should.

Absolutely check your Code of Ethics policy, most address this issue. And I agree 100% with Randy, I think it's a major conflict of interest.

our handbook allows for outside employment, but does not allow at 1) bars 2) casinos 3) any other financial institution.

huge conflict of interest

Agree with the above, but my own start in the banking industry in the mid 90's actually found me in this situation. I was a seasonal teller for summer and Christmas at a bank in my home town and "reverse seasonal teller" for a bank close to school the rest of the year. Technically I was employed at both banks at the same time, but I was not working a teller drawer during the same time period. Considering where that start has taken me, I am thankful to each institution for giving me that start.