Commonly witnesses may invoke the fifth amendment to avoid incriminating testimony, but can the fifth be invoked to refuse production of documents (for example e-mails) that may incriminate. Could the fifth be invoked to prohibit production of bank records that may incriminate?
In a landmark document-production case, Fisher v. United States, 425 U.S. 391, it was held that
The Fifth Amendment does not independently proscribe the compelled production of every sort of incriminating evidence, but applies only when the accused is compelled to make a testimonial communication that is incriminating
A subpoena served on a taxpayer requiring him to produce an accountant's workpapers in his possession without doubt involves substantial compulsion. But it does not compel oral testimony; nor would it ordinarily compel the taxpayer to restate, repeat, or affirm the truth of the contents of the documents sought. Therefore, the Fifth Amendment would not be violated by the fact alone that the papers, on their face, might incriminate the taxpayer, for the privilege protects a person only against being incriminated by his own compelled testimonial communications...The taxpayer cannot avoid compliance with the subpoena merely by asserting that the item of evidence which he is required to produce contains incriminating writing, whether his own or that of someone else.
By way of background (and as cited by the Fisher court), Schmerber v. California, 384 U.S. 757 where the accused was intoxicated and blood was drawn involuntarily, the court held that
The privilege against self-incrimination is not available to an accused in a case such as this, where there is not even a shadow of compulsion to testify against himself, or otherwise provide the State with evidence of a testimonial or communicative nature.
In other words, the self-incrimination clause is about actual testimony, and not other physical acts (such as fingerprints, DNA, records) which are used as evidence of guilt.
The witness could plead the fifth during questioning. However, the government could seize incriminating information from the bank, or email/other service provider, through a search warrant or a subpoena. They can also get a search warrant to discover these documents in your residence.
According to the Right to Financial Privacy Act (12 U.S.C. § 3402):
Except as provided by section 3403(c) or (d), 3413, or 3414 of this title, no Government authority may have access to or obtain copies of, the information contained in the financial records of any customer from a financial institution unless the financial records are reasonably described and --
(1) such customer has authorized such disclosure in accordance with section 3404 of this title;
(2) such financial records are disclosed in response to an administrative subpoena or summons which meets the requirements of section 3405 of this title;
(3) such financial records are disclosed in response to a search warrant which meets the requirements of section 3406 of this title;
(4) such financial records are disclosed in response to a judicial subpoena which meets the requirements of section 3407 of this title; or
(5) such financial records are disclosed in response to a formal written request which meets the requirements of section 3408 of this title.