Gov. Andrew Cuomo’s coverup of nursing-home COVID deaths was even worse than we’d thought: It turns out his Department of Health started collecting the key data a full year ago — even as it kept the info secret in defiance of lawmakers’ rights as well as the Freedom of Information Law. A DOH memo obtained by The Post shows the department began ordering care homes to report both in-home and in-hospital deaths of residents last April. Yet for nine months Team Cuomo refused to share it, with Health Commissioner Howard Zucker insulting legislators with bogus claims the info wasn’t accurate enough to release and other staffers falsely claiming they couldn’t compile the info to comply with FOIL requests from the Empire Center. In January, Attorney General Tish James finally called out the clear signs that total deaths were half again what Team Cuomo was pretending — and only then did DOH release the true tally. The conspiracy was all about hiding the evidence of a deadly scandal: Zucker’s March 25, 2020, order forced homes to admit COVID-contagious patients without even testing them.