State health officials refuse to say if they’re investigating a Long Island nursing home that reported just four COVID-19 deaths, although many more people died there during the height of the pandemic.

The Post revealed that 35 people died from all causes at the Grand Rehabilitation and Nursing at South Point in Island Park in the three-month period between March 1 and May 31, 2020, compared to just three in the same period a year earlier.

Grand Rehabilitation had reported one COVID-19 death at the home to the Department of Health and three others at a hospital.

The DOH had told The Post it was “reviewing all data received,” but would not comment on whether it was specifically probing this nursing home for undercounting deaths.

A DOH spokesman later said that COVID-19 was listed on the death certificates of three people who died at the nursing home, either as a contributing factor or probable contributing factor. The spokesman still would not comment on whether it would take any action against the home for underreporting the deaths.

The Cuomo administration has been wrapped up in a scandal about the accuracy of nursing home death counts that started last month when Attorney General Letitia James released a report estimating the tally would increase by more than 50 percent if it included residents who died in hospitals.

Then federal investigators opened an inquiry on Gov. Cuomo’s handling of nursing homes during the pandemic after The Post reported that his administration withheld data on the deaths from state lawmakers.