Both of the responses received are good, but they ignore one CRITICAL issue, that of 'permissable' purpose.
Over the last few years, the Fair Credit Reporting Act has been revised to further restrict access to individual credit reports.
Here is an excerpt from the current FCRA as to who may access someone elses credit report.
"§ 604. Permissible purposes of consumer reports [15 U.S.C. § 1681b]
(a) In general. Subject to subsection (c), any consumer reporting agency may furnish a consumer report under the following circumstances and no other:
(1) In response to the order of a court having jurisdiction to issue such an order, or a subpoena issued in connection with proceedings before a Federal grand jury.
(2) In accordance with the written instructions of the consumer to whom it relates.
(3) To a person which it has reason to believe:
(A) intends to use the information in connection with a credit transaction involving the consumer on whom the information is to be furnished and involving the extension of credit to, or review or collection of an account of, the consumer; or
(B) intends to use the information for employment purposes; or
(C) intends to use the information in connection with the underwriting of insurance involving the consumer; or
(D) intends to use the information in connection with a determination of the consumer's eligibility for a license or other benefit granted by a governmental instrumentality required by law to consider an applicant's financial responsibility or status; or
(E) intends to use the information, as a potential investor or servicer, or current insurer, in connection with a valuation of, or an assessment of the credit or prepayment risks associated with, an existing credit obligation; or
(F) otherwise has a legitimate business need for the information
(i) in connection with a business transaction that is initiated by the consumer; or
(ii) to review an account to determine whether the consumer continues to meet the terms of the account.
(4) In response to a request by the head of a State or local child support enforcement agency (or a State or local government official authorized by the head of such an agency), if the person making the request certifies to the consumer reporting agency that
(A) the consumer report is needed for the purpose of establishing an individual’s capacity to make child support payments or determining the appropriate level of such payments;
(B) the paternity of the consumer for the child to which the obligation relates has been established or acknowledged by the consumer in accordance with State laws under which the obligation arises (if required by those laws);
(C) the person has provided at least 10 days’ prior notice to the consumer whose report is requested, by certified or registered mail to the last known address of the consumer, that the report will be requested; and
(D) the consumer report will be kept confidential, will be used solely for a purpose described in subparagraph (A), and will not be used in connection with any other civil, administrative, or criminal proceeding, or for any other purpose.
(5) To an agency administering a State plan under Section 454 of the Social Security Act (42 U.S.C. § 654) for use to set an initial or modified child support award."
In your case (tenant screening), this means that you have to have the applicants WRITTEN permission to access his/her credit history. If you don't have it, you and the provider, could be in violation of federal law.
Here is a link to the entire FCRA:
http://www.ftc.gov/os/statutes/fcrajan2002.pdf
and to the FTC website:
http://www.ftc.gov/os/statutes/fcrajump.htm