Anyone know is the USPS allows employees to have tattoos?

I do not believe there is a specific policy regarding tats but you are to present a clean professional appearance. So it would be up to whoever is interviewing you for the position. Hiring authorities have a lot of discretion as to what presents a professional appearance.

I had worked in the Computer Forwarding Service for 14 years and did not notice many people with tattoos. I'm sure there were some people having them, but paid no mind. Ask your letter carrier or go to a post office and ask a clerk.

Yes