Washington State uses the CSTE definition https://preparedness.cste.org/wp-content/uploads/2022/12/CSTE-Revised-Classification-of-COVID-19-associated-Deaths.Final_.11.22.22.pdf  effective on 1/1/2023.   Previous to 1/1/2023, both a death certificate and a positive test result were required.   

Minnesota's current definition is also CSTE's. I attached a file with the info I copied from our web site.
Mortality (Death) Data COVID-19 Situation Update - MN Dept. of Health (state.mn.us)

MN COVID Death Data definitions 5.1.24.docx 16.5 KB • Download

Illinois ultimately uses the CSTE definition (revised classification) as well, for deaths occurring on/after 09/01/2022:
In a confirmed or probable COVID-19 case within the last 12 months, the case will be considered a COVID-related death if the case meets the national case definition's vital records criteria for reporting, i.e. - If disease (COVID-19 or SARS-CoV-2 or an equivalent term) is listed on the death certificate as an:
(1) Immediate Cause of Death,
(2) Underlying Cause of Death, or
(3) Significant Condition Contributing to Death

Local health departments may utilize other evidence (e.g., clinical history, medical records, or autopsy findings) to update state surveillance records and cause of death on a case-by-case basis.

If COVID is listed on a death certificate but no COVID case exists within the past 12 months for a patient a new case will be created:
- for deaths occurring before 1/1/2023, probable case records were created
- for deaths occurring 1/1/2023 and later: patients without confirmatory testing are counted as suspect COVID cases and not reported in statewide COVID-19 deaths.

IDPH CD Topics - COVID-19 - Deaths due to COVID-19.docx 127 KB • Download

According to our respiratory death webpage (https://ldh.la.gov/page/respiratory-death-data): "To align with a national standard, on September 1, 2023, the Louisiana Department of Health adopted the CSTE Revised COVID-19-associated Death Classification Guidance for Public Health Surveillance Programs. This revised COVID-19-associated case definition counts deaths where a death certificate indicates COVID-19, or an equivalent term, as a cause or contributor to death, with or without laboratory evidence for SARS-CoV-2. This definition will apply to individuals >18 years of age and will also apply to influenza and RSV-associated deaths."