@eques,
Sure you can say that. It's a fine statement in English. I was just suggesting a little more methodical approach. Some landlords may dislike this type of inquiry and it might sometimes be prudent to "soften them up" a little before getting to the important questions. But I'm no expert. Whatever works for you.
English-wise I might make a couple of other suggestions. It might be better to rephrase it since you're actually asking two questions, one of which may be moot, depending on the answer to the first. For example
Quote: "I'd like to one of your tenant's tenancy status, and, if he is a current tenant, I'd like to ask if his rent is current."
Also "tenancy status" refers to the question of whether the person in question actually is a tenant. For this reason, it's also best not to refer to "one of your tenants" at the outset. It is redundant to ask about a "tenant's" tenancy status. Identifying the person as a "tenant" presumes you already know his "tenancy status." If you already know, or assume, you know that, then it's best to leave out "tenancy status." For example:
Quote: "I'd like to ask if one of your tenants is current in his rent."