Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
For purposes of this answer, I assume that you are referring to a pre-employment background check.
Background checks are often requested by employers on job candidates. Pre-employment background reports are usually compiled from several different databases and include information related to criminal records, commercial records and financial records and, in certain instances, past employment. Because the reports are compiled from several different sources, a complete report is not something that can be requested from the county clerk. While certain information on the report may be obtained from the county clerk (e.g., real property records or liens against real property due to outstanding judgments), a complete "background check" cannot be obtained from the county clerk.
Prospective employers use the services of third-party companies to order background checks. If you recently applied for a job and the prospective employer conducted a background check, you can request a copy of the report from the prospective employer. Alternatively, there are several third-party services online that you can order a report (e.g., www.backgroundchecks.com and www.intelius.com)