A landlord could run a background check on you if they have your information even without you knowing.
Some landlords will run background checks on tenants every year or so without their permission and will then kick the tenant out due to things found on the background check.
However according to landlord and tenant laws it's not legal for a landlord to run a background check without the tenants written permission.
When a tenant applies for an apartment or rental place then the landlord or property manager will get written permission from the tenant to run a background check on them.
That should be the only time a landlord or property manager runs a background check on the tenant.
Applicants must also be provided with a summary of their rights under the Fair Credit Report Act (FCRA) before any credit reports are pulled.