The police department in Wilmette, Illinois said it was "seeking to check the well-being of Sinead O'Connor."
The singer "reportedly left the Wilmette area for a bicycle ride yesterday (Sunday) at 6 am (1100 GMT) and has not returned," it said in a statement.
The police department, where officials said they had no further information, said that a caller had reached out to voice concerns after seeing the 49-year-old singer on the bicycle.
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The singer's publicist did not immediately reply to an AFP request for comment.
O'Connor, who has always been known for her strong views, has recently posted a string of messages on Facebook that have raised alarm.
In her most recent posting, O'Connor appeared to be asking her son to go to court on Tuesday to take custody of his brother.
Late last year, she suggested on Facebook that she had tried to kill herself in an overdose.
It was unclear why O'Connor was in the United States but she recently said she planned to protest in North Carolina, a likely reference to the southern state's recent law to restrict the rights of transgender people.
O'Connor also recently wrote that comedian Arsenio Hall had been providing drugs for decades to late pop icon Prince, leading Hall to express outrage and sue for libel.
Prince, who died on April 21, wrote O'Connor's best known song, the ballad "Nothing Compares 2 You."
O'Connor won critical acclaim for her haunting voice but frequently entered controversies.
She has spoken of being abused as a child and has vociferously criticized the Roman Catholic Church for not doing more to protect minors.
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