Possibly, but to my knowledge there's no precedent allowing or disallowing prosecution of a sitting US president on the state level. This in contrast to prosecution at the federal level, which is not possible because of an opinion by the Office of Legal Counsel (OLC). While the word opinion may sound subjective, the OLC's task is characterised as follows on its own website:
OLCs core function, pursuant to the Attorney General's delegation, is to provide controlling advice to Executive Branch officials on questions of law that are centrally important to the functioning of the Federal Government. In performing this function, OLC helps the President fulfill his or her constitutional duties to preserve, protect, and defend the Constitution, and to “take Care that the Laws be faithfully executed.” It is thus imperative that the Office's advice be clear, accurate, thoroughly researched, and soundly reasoned. The value of OLC advice depends upon the strength of its analysis.
The OLC opinion that prevents bringing charges against a sitting president on the federal level is entitled A Sitting Presidents Amenability to Indictment and Criminal Prosecution. The 39-page memo starts with:
In 1973, the Department concluded that the indictment or criminal prosecution
of a sitting President would impermissibly undermine the capacity of the executive
branch to perform its constitutionally assigned functions. We have been asked
to summarize and review the analysis provided in support of that conclusion, and
to consider whether any subsequent developments in the law lead us today to
reconsider and modify or disavow that determination.1 We believe that the conclusion reached by the Department in 1973 still represents the best interpretation
of the Constitution.
On the second page of the memo there's an important footnote saying that the analysis only applies to the federal level (emphasis mine):
Implicit in the Department’s constitutional analysis of this question in 1973 was the assumption that the President
would oppose an attempt to subject him to indictment or prosecution. We proceed on the same assumption today
and therefore do not inquire whether it would be constitutional to indict or try the President with his consent.
The Department’s previous analysis also focused exclusively on federal rather than state prosecution of a sitting
President. We proceed on this assumption as well, and thus we do not consider any additional constitutional concerns
that may be implicated by state criminal prosecution of a sitting President. See Clinton v Jones, 520 U S 681,
691 (1997) (noting that a state criminal prosecution of a sitting President would raise “ federalism and comity”
concerns rather than separation of powers concerns)