We didn't hire an applicant based on his background screening. He has sent me an email asking me why we didn't hire him. What is the best way to respond?

You have no obligation to respond either way.

Simply say that it's a very competitive market, you had some very strong applicants, and decided that there were others who were a better match for the job. Wish him best of luck in his endeavors.

Simply indicate that you selected the best-qualified applicant.

"Thank you for your inquiry and interest in working for our company. We have narrowed down a list of other applicants who meet our desired attributes and experience, and (have, have not) chosen one.

Should we have openings in the future, your application will be on file."

I would not include this line:



"Should we have openings in the future, your application will be on file."

I wouldn't say anything in the rejection letter that isn't absolutely true. Perhaps it depends on the hiring practices in your company, but in my experience whenever advertising for a new hire we never go back and look at old applications of people we have previously passed over. Of course they're free to apply again, but we don't search them out.

I would not include this line:



I wouldn't say anything in the rejection letter that isn't absolutely true. Perhaps it depends on the hiring practices in your company, but in my experience whenever advertising for a new hire we never go back and look at old applications of people we have previously passed over. Of course they're free to apply again, but we don't search them out.

True, but a lot of companies say that as (supposedly harmless) appeasement, even though I agree that none of them go back to old applications.
There's an old saying in business: Be polite, because someday that person may be your boss.
And there's something a little troubling about someone who asks why he or she wasn't hired. I wouldn't want someone going off the deep end.

All of this is, strictly speaking, not a "legal" answer. Legally, OP's company (if it is a company and not a governmental agency) can hire whoever it pleases, except that it cannot discriminate on the basis of race or certain other prohibited criteria. If it is a government agency, that might be different. And OP has no legal obligation to even respond to the "why didn't you hire me?" question.