Can rabbits give a person Tuberculosis?

No not that ,,However they can other issues ;;;

Lice, fleas and ticks.all can come from the rabbit.

Pasteturellosis ; is a bacterial infection cause respiratory issues.

Tularemia by an infected bunny or by insect bites, rabbit scratches and direct contact.

Allergys from a rabbits fur or saliva and causes respiratory issues

Dermatophytosis infection of the skin by direct contact by fur and is a fungal infection ( if the bunny is infected.)

look out for loss of appetite, bloating, change in color and consistency of waste and production of more salivation.

Its wise to keep in seprate cages so can monitor the rabbits healthif have several together you may not know which one is ill.

I guess if you let them inside your body.