Each landlord is different, some check different databases. It really depends on the particular landlord or management company.
No legal advice is given here. My responses to questions on Avvo are never intended as legal advice and must NOT be relied upon as if they were legal advice. I give legal advice ONLY in the course of a formal attorney-client relationship. Exchange of information through Avvo's Questions & Answers forum does not establish an attorney-client relationship with me. That relationship is established only by joint execution of a written agreement for legal services. I am only licensed in the States of California and New York and the District of Columbia
No lawyer can tell you how thoroughly some other person / entity will go in conducting a background check.
That said, unfortunately, in the digital age your criminal record remains with you forever. To some degree or another this is true regardless of whether your ultimately seal or expunge a case. All arrests are natters of public record, and, even if removed from the public record they remain in private records This is one down-side to technology.
You might want to do your own background check to see what pops up. Forewarned is forearmed.
I hope this has been helpful to you.
First, second and third: No attorney-client relationship exists by virtue of any Q&A with Michael A. Haber, Esq. on Avvo. Fourth: Anything that you post on Avvo (or on similar sites) or on any social media is by its nature public. It is essentially an admission / confession and can be introduced into evidence as a statement against your interest in a subsequent legal proceeding. Once posted you lose any reasonable expectation of privacy, so, as this is an open forum (with no privilege attached), please be extra careful when considering what to post online (forewarned is forearmed.)
The extent of the background check is dependent on the person or agency that conducts the search. There is no time limit involved. It is within the discretion of the apartment complex to accept or reject the applicant.
This answer/response is based on the information provided in the question asked and requires a much more complete context than is available in this public forum.
Please do NOT use this answer/response to say or do anything regarding your situation.
BEFORE you say or do anything consult with an experienced Federal and/or state criminal defense attorney in your jurisdiction who will listen to you and your concerns.