A detective took the statement from Dr Jane Hamilton this week after The Herald reported the psychiatrist's claims that NHS Lothian managers attempted to prevent her repeating her concerns about a hospital's mother and baby unit.
The police's involvement emerged as Scottish Health Secretary Alex Neil yesterday declared he was removing confidentiality clauses from settlements with NHS staff.
Mr Neil said that despite a clear difference between gagging and confidentiality clauses in contracts, he accepted there was a perception they "could be used to prevent staff from speaking out about failures in care offered to patients".
Dr Hamilton had raised her fears about the mother and baby unit at St John's Hospital, Livingston, and warned in writing that somebody could die. Two mothers subsequently took their own lives and the family of one is suing the health board.
Yesterday, Dr Hamilton said the legal advice she received about the settlement her health board first offered her was that she was "effectively being gagged".
She risked losing a six-figure payout by speaking of her refusal to sign a severance agreement.
Dr Hamilton added: "I had a visit from the police this week and it is clear they are taking it seriously, because any agreement that seeks to prevent staff from raising concerns about patient safety or malpractice would be illegal.
"The detective was with me for almost two hours. He took copious notes and wanted to go through everything from the very start - what my clinical concerns were and what my experiences had been. He asked me whether I had felt gagged by the contract document I was offered, and I said I most certainly had done."
Meanwhile, campaigners, including psychiatric nurse turned whistleblower Rab Wilson, who exposed failures in NHS Ayrshire and Arran, and the organisation Patients First Scotland have welcomed Mr Neil's announcement.
A new agreement will be drafted for health boards to use when reaching financial settlements with staff that will not automatically include a confidentiality clause.
Settlement agreements are legally binding deals in which an employee accepts payment in exchange for waiving the right to pursue legal action against their employer. In the last five years Scottish health boards have made 697 settlements with NHS workers, with the vast majority containing a confidentiality section.
The Scottish Government's new settlement agreement will not include any confidentiality clauses, unless both the employee and the board explicitly agree to one. Boards will have to make a presumption against gagging.
A Government spokeswoman said staff who had already signed deals could potentially renegotiate confidentiality clauses.
A support team to help deal with issues of bullying and harassment in the NHS is also being established.
Mr Wilson, who had petitioned the Scottish Parliament to scrap gagging clauses, described Mr Neil's announcement as "brilliant".
He said: "People have been paid off with public money and they feel they cannot tell their stories. This hangs over your conscience."
Jill Vickerman, Scottish secretary of the British Medical Association, welcomed the move but said they still supported confidentiality clauses in settlement agreements to protect personal information.
NHS Lothian has repeatedly given assurances that Dr Hamilton's concerns, first raised in 2007, have been fully investigated and found to be without foundation, and that there has been no attempt to gag her.
The board would not comment.
A police spokesman said: "This inquiry is at an early stage and officers have yet to determine whether any criminal activity has taken place."