Yes, technically this is legally permissible to do, but doing so may not be a good idea. First, the company where she is currently working may not know she is job searching. In fact, in all likelihood, they probably do NOT know she is job searching. You do not want to be the one to bring that to their attention.
Companies should have a job application that specifically asks if it is OK to contact the applicant’s current employer. If not, you can ask about that during a job interview—but it still would be prudent not to contact a current employer without the applicant’s permission. It also may be that the applicant has told certain people who have agreed to act as references that she is job hunting, but has not told others—including the applicant’s boss or human resources.
Once you call references (whether those listed by the applicant or others who work with the person), those people are likely to tell the applicant that they were contacted. That usually means to people that you are seriously considering hiring them. For that reason, we generally recommend against contacting references for anyone other than those you really are considering hiring, which you do not know before you interview them.
At the interview, you may determine that the applicant is not right for your organization. At that point, you wouldn’t contact anyone or move the process forward. You then would not need to deal with any of the issues referenced above.
If you interview this applicant, like her, and would consider hiring her, then, yes, you can contact anyone you like whether they are “named” references or not – except for people at her current employer if she’s asked you not to contact them because they do not know she’s job searching.
