Our credit check is a hard pull on the tenant applicant's credit. The only time a credit pull is considered a "soft pull" is when the consumer pulls the report on themselves. Anytime a report is ran for a credit related reason (vehicle purchase, credit card, housing, employment, etc.) the credit bureaus need to identify the purpose of the pull.
Pulling your credit report once for a specific reason, like housing, should have no impact on a credit score. It is only when the credit bureaus see multiple attempts in the same time period for the same type of inquiry, that will trigger a "too many inquires" code and potentially cause a drop in a credit score.