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About a year ago, when Alvin Bragg, the Manhattan district attorney, indicted former President Donald Trump, I was critical of the case and called it an embarrassment. I thought an array of legal problems would and should lead to long delays in federal courts.

After listening to Monday’s opening statement by prosecutors, I still think the Manhattan D.A. has made a historic mistake. Their vague allegation about “a criminal scheme to corrupt the 2016 presidential election” has me more concerned than ever about their unprecedented use of state law and their persistent avoidance of specifying an election crime or a valid theory of fraud.

To recap: Mr. Trump is accused in the case of falsifying business records. Those are misdemeanor charges. To elevate it to a criminal case, Mr. Bragg and his team have pointed to potential violations of federal election law and state tax fraud. They also cite state election law, but state statutory definitions of “public office” seem to limit those statutes to state and local races.

Both the misdemeanor and felony charges require that the defendant made the false record with “intent to defraud.” A year ago, I wondered how entirely internal business records (the daily ledger, pay stubs and invoices) could be the basis of any fraud if they are not shared with anyone outside the business. I suggested that the real fraud was Mr. Trump’s filing an (allegedly) false report to the Federal Election Commission, and only federal prosecutors had jurisdiction over that filing.

A recent conversation with Jeffrey Cohen, a friend, Boston College law professor and former prosecutor, made me think that the case could turn out to be more legitimate than I had originally thought. The reason has to do with those allegedly falsified business records: Most of them were entered in early 2017, generally before Mr. Trump filed his Federal Election Commission report that summer. Mr. Trump may have foreseen an investigation into his campaign, leading to its financial records. Mr. Trump may have falsely recorded these internal records before the F.E.C. filing as consciously part of the same fraud: to create a consistent paper trail and to hide intent to violate federal election laws, or defraud the F.E.C.

In short: It’s not the crime; it’s the cover-up.

Looking at the case in this way might address concerns about state jurisdiction. In this scenario, Mr. Trump arguably intended to deceive state investigators, too. State investigators could find these inconsistencies and alert federal agencies. Prosecutors could argue that New York State agencies have an interest in detecting conspiracies to defraud federal entities; they might also have a plausible answer to significant questions about whether New York State has jurisdiction or whether this stretch of a state business filing law is pre-empted by federal law.