Under Hawaii law a judge can order release of the original birth certificate for inspection and since Congressional Subpoenas have the legal force of a judge’s court order, an investigative committee of either House of Congress could issue a subpoena for the original birth certficate for inspection; but Congress hasn’t been interested.
If anyone wanted to try to impeach the statements issued by Hawaii officials, those current and former officials could be deposed under oath or called to testify under oath in a court of law, before a Grand Jury or before a committee of Congress.
True. But the "big picture" view here, as you well know, means that there's little reason for anyone in a decision-making position to have reason to question the Hawaiian officials' statements affirming Obama's Hawaiian birth. Such statements are consistent with near all of the documentary evidence as to Obama's birth (the newspaper announcements, INS and State Dept. files, the Indonesian school application, 1990 newspaper articles, etc.)
Apart from the 1991 agency bio, there is precious little documentary evidence suggesting a non-Hawaiian birth. (And in light of the national publications the year prior all reporting an Hawaiian birth, it's not credible to think the agency piece was other than the error the agency has acknowledged.)
The great preponderance of the evidence points to birth having been in Hawaii. The COLB, Long-form, and Hawaiian verifications are simply the more formal and official items of proof.