Sure as can neighbors, family or friends too...

Resident or Owner? Look at the HOA documents for a hint. 

Whose house? This question has more answers than grains of sand on the beach. What's in the bylaws?

Probably, if they are accessing the house of the resident that is making the request.  Seems like there may be more to the question than is explained here...

Richie Alan Naggar has this correct. Anyone can access a house if requested or invited by the resident. A tenant resident might be different so sort of depends on whether it's an owner resident or a tenant resident.

Bo Zivak ZI think you need to state an example as to the circumstances because the answer to the question asked is: NOI! Maybe? Yes

Really need more info here.  

Check the Governing Documents, including all rules and policies, as well as the laws that may trump the docs depending on how old they are. 

Be sure also to be clear on "definitions" as defined in the documents. 

You need to explain further Bo Zivak . As in can a lender set up a lenders open house?????

Sure, Ian the Vice pres of my Hoa and only one of a few that live here full time.  I do it routinely on request to check after storms, etc, etc.

what?

I would guess a resident can allow anyone into their home that the want to let in.

Sorry but I don't understand the underlying scenario to be able to respond. 

 What house, and for what reason?    

Consult a lawyer.

Not without cause so ?