She also stated that the European referendum result meant “Ireland is officially no longer owned by Britain”.
A spokesman for the Chicago Police Department said the force was alerted at 3.30pm local time that the whereabouts of the 49-year-old Irish singer were unknown.
Officers received a report from police in Ireland that O’Connor had said she planned to jump off a bridge in the US city, the spokesman said.
In her Facebook update, the Nothing Compares 2 U singer said she was “far too f****** happy” to jump off a bridge.
She accused “some stupid bitch up at Swords Garda station” of spreading the suicide report.
O’Connor congratulated “every man, woman and child who ever died for the cause of Irish freedom” in her post.
The 49-year-old also had an “our day has come” message to “all those, including myself, who have been persecuted mercilessly by the Irish so-called free-state for having declared support for Sinn Fein and the Republican movement”.
The message concluded: “Ireland 4 England 0”.
O’Connor’s history of mental health problems sparked a police search in May when she failed to return from a bike ride in the Chicago suburb of Wilmette.
In December, she wrote on Facebook that she had been detained in hospital for a mental health evaluation.
A month earlier she wrote another Facebook post claiming she had overdosed on pills in a hotel room in Ireland.
She was later found safe and taken to hospital.
