When you hire a nanny, you should recognize that you are an employer. As an employer you are regulated by the Fair Credit Reporting Act (FCRA). This requires you to get the job applicant's written permission before you purchase a pre-employment background check.
It is easy to get their permission, just include a permission form or short paragraph in their job application, that they will sign when they fill out you job application. And yes, you definitely should have a job application, and have them fill it out in front of you. Otherwise, they can take it home and make up a bunch of plausible sounding lies. Also, if they object to the background check, then you do not want to hire them.
If you find out anything bad about them that influences you not to hire them, then the FCRA requires that you tell them what it is and where you got it.
However, if you do not purchase a background check, then you do not have to get their permission. You can research all you want on your own. You can learn
How to Do a Free Background Search
, here. For a free criminal background check, the basic process is that you look at the job application to find out in what cities and counties they have lived, then you go to the government web sites in those locales and search their criminal records. Some government web sites offer the information for free, and some charge a small fee. The complexity arises because there is no government database that covers the entire nation, which is open to the public. So, if they could have lived in other locations (which they may hide), then you can use a private company that specializes in nationwide background checks. So, if you purchase a
pre-employment background search
, then the FCRA applies.