In Washington State, "cause of death" is part of a Vital Record under RCW 70.58, specifically a death certificate. RCW 70.58.170 says who may file a death certificate: "The funeral director or person having the right to control the disposition of the human remains under RCW 68.50.160 shall file the certificate of death or fetal death". That person
shall present the certificate of death to the physician, physician's
assistant, or advanced registered nurse practitioner last in
attendance upon the deceased, or, if the deceased died without medical
attendance, to the health officer, medical examiner, coroner, or
prosecuting attorney having jurisdiction, who shall certify the cause
of death according to his or her best knowledge and belief and shall
sign or electronically approve the certificate of death or fetal death
within two business days after being presented with the certificate
unless good cause for not signing or electronically approving the
certificate within the two business days can be established.
So there are many people who might be presented with the certificate, but no judges or juries. "Cause of death" is part of the information entered on the death certificate.
When a person dies "without medical attendance", RCW 70.58.180 is applicable. In that case, the person disposing of the body "shall notify the coroner, medical examiner, or prosecuting attorney if there is no coroner or medical examiner in the county".
If the death is not suspicious,
the person so notified completes and signs the form, noting lack of attending medical practicioner, and notes cause of death without an autopsy, relying on "statements of relatives, persons in attendance during the last sickness, persons present at the time of death or other persons having adequate knowledge of the facts".
If the circumstances suggest that the death or fetal death was caused
by unlawful or unnatural causes or if there is no local health officer
with jurisdiction, the coroner or medical examiner, or the prosecuting
attorney shall complete and sign or electronically approve the
certification, noting upon the certificate that no physician,
physician's assistant, or advanced registered nurse practitioner was
in attendance at the time of death.
In either case,
The cause of death, the manner and mode in which death occurred, as
noted by the coroner or medical examiner, or if none, the prosecuting
attorney or the health officer and incorporated in the death
certificate filed with the department shall be the legally accepted
manner and mode by which the deceased came to his or her death and
shall be the legally accepted cause of death.
So: the law allows many people (in a hierarchy) to provide the legal cause of death, which shall be recorded on the certificate of death.
The statute pertaining to county coroners potentially broadens the scope of cause of death a bit. A county coroner has the power to hold an inquest into a suspicious death. Then, RCW 36.24.070 states that
After hearing the testimony, the jury shall render its verdict and
certify the same in writing signed by the jurors, and setting forth
who the person killed is, if known, and when, where and by what means
he or she came to his or her death; or if he or she was killed, or his
or her death was occasioned by the act of another by criminal means,
who is guilty thereof, if known.
There is nothing in the statute that specifically mandates that the coroner "accept" the verdict of the jury. Some details are left to county-specific procedure, this being the law for King County. This finding is separate from the medical / vital records concept of "cause of death".
In other words, whoever fills out the death certificate provides the legal cause of death.