How to investigate the Cheryl Mills claim of attorney-client privilege with Hillary

Cheryl Mills sat in on Hillary Clinton’s FBI interrogation – a highly irregular procedure, given her status as a material witness and possible suspect.  This foreclosed the common investigative procedure of questioning witnesses separately and leveraging the differences in their stories.  The basis for this was the claim that Mills was also Hillary’s personal attorney.

Whether Cheryl Mills was ever Hillary Clinton's attorney could be resolved by asking her to produce their retainer agreement.  In the District of Columbia and most other jurisdictions, a lawyer must have a written agreement with a person in order to act as his lawyer.  Lawyers are also required to keep contemporaneous records of their time.  Neither of these things is privileged, and courts have ordered lawyers to produce them to the other side when issues of representation arise.

If this were in front of a judge instead of a corrupt agency, you could argue that if there is no evidence of an attorney-client relationship (mainly the retainer agreement), then there is no privilege.  Mills is certainly not the first lawyer to invoke the privilege to hide her own criminal conduct.  A judge could easily deal with this issue, but for some reason the FBI cannot.  A grand jury should have been convened, rather than the very weak investigation done by the FBI, which seemed designed to fall short from the beginning.

I'm not sure a congressional investigation will be any better, but Ms. Mills should not be allowed to get away with this without some proof of her legal representation.

Author's Update:

Rule 1.5(b) of the D.C. Rules of Professional Conduct, which applies to retainer agreements, states: “[w]hen the lawyer has not regularly represented the client, the basis or rate of the fee, the scope of the lawyer’s representation, and the expenses for which the client will be responsible shall be communicated to the client, in writing, before or within a reasonable time after commencing the representation.”  Regardless of any fee arrangement, Mills would have had to communicate the scope of the representation to Clinton, in writing.
It's true that an attorney-client relationship can be formed by accident, if a person mistakenly believes that an attorney is representing them. Although it's conceivable that this occurred between Mills and Clinton, Mills would still have had an ethical duty to reduce their understanding to writing within a reasonable time. Both Mills and Clinton are attorneys, and are expected to know these rules.
With respect to refusing to answer questions, the party asserting a privilege bears the burden of proof.  Absent a retainer agreement, Mills would have to prove this through other evidence, such as time keeping records. If there is no evidence, other than Mills' self-serving statements, I don't think she could meet the burden of proof.