As far I've understood your question my response will be
There are professional services who do background verification/auditing of individuals and gather the information to cross verify it. So it itself is a service offering apart from the application you want to use it for (long story short you don't wanna do it just for the sake of your app/service, if you think of it as new business opportunity then it's a different ballgame and out of scope for this question)
There are two major types of background verifications 1. Criminal/personal records 2. Financial/credit verification records
Based on the requirements the details comprising of these records vary.
I am unsure about service providers for criminal/personal records your area (as these will be domestic/country specific agencies) however for financial/credit verification records you can tie up with Experian, Equifax etc service providers(again country specific considering the legal aspect of capturing part of PII).
Oh and be advised when you will be embedding/engaging their services in your application you need to adhere the guidelines for how you'll protect the data at rest and in transit, have to go through their independent audits like Experian Independent 3rd party assessment (EI3PA), Equifax audit etc which are as strict as PCI audits and need to be executed by independent QSA annually.
Finally following are some of the companies (with better SEO at least) who will be able to do the job for you.
(Might be deprecated) Consumer Authentication Service by VeriSign - http://xml.coverpages.org/VerisignCAS.html
i-Verified Background Screening Solutions: http://i-verified.us/
ACCESS BACKGROUND SCREEN LLC: http://www.accessbackgroundscreen.com/id9.html
Credit Verification: http://www.creditverification.com/
einvestigator has a list ofprivate investigators if required: https://www.einvestigator.com/missouri-private-investigators/
A parting gift, few valuable links which maybe helpful either now or in future.
Hope this helps in anyway possible.