POLICE are to reopen their investigation into the death of the wife of former Hong Kong minister Lord Caithness following a riddle over the time of the fatal gunshot. They intend to look into an apparent time difference between the time of the shooting given by Lord Caithness and evidence from a former inquest witness who put it three hours later. The parents of Lady Caithness have also written to police complaining about faults with the inquiry. The former Hong Kong minister, who was having an affair at the time of the shooting, said he last saw his wife alive as he played cards with his daughter at 6.20 pm [UK time] on January 8. He told the inquest Lady Caithness killed herself at their Oxfordshire home at 6.30 pm. However, a neighbour heard ''a loud bang like a gunshot'' at about 3 pm. The doctor called to tend to 40-year-old Diana said he was called at 6 pm and by the time he arrived at 6.30 pm she appeared to have been dead for about three hours. The inquest should have closed the tragedy for the earl, who resigned from his post as transport minister soon after the shooting. But Detective Chief Superintendent Tom Morrison of Thames Valley Police said: ''Issues of concern have been raised by the [countess'] family which were not dealt with at the inquest. ''Thames Valley Police are reviewing the original investigation to determine whether those concerns can be satisfied.'' It seems likely that the earl may face further police questioning as a result of the different timings. He told the inquest his wife shot herself as he was playing cards with his 15-year-old daughter Lady Iona. ''At about 6.20 pm my wife saw that we were playing and went upstairs. About 10 minutes later we heard a dreadful noise.'' Neighbour Jane Lambert told the inquest that she heard a loud noise about three hours earlier. In a statement she said: ''Between 3 pm and 3.30 pm I heard a loud bang like a gunshot. It seemed quite close by. I would not say it was the sound of a car backfiring.'' The family doctor and friend, Dr John Goves, told the inquest he received a distressed call from Lord Caithness at 6 pm. He arrived at the house at 6.30 pm and the state of the body indicated she had been dead about three hours. Lady Caithness' parents find it hard to believe that their daughter could have become suicidal even though she was distressed about the Earl's affair with Jan Fitzalan-Howard, a socialite who had worked for both the Tory Party and Princess Anne. It appears the police may want to turn the spotlight on a row the couple had on the morning of the shooting. The earl told the inquest: ''We had a discussion about the future in the morning which had been quite heated. She had been upset.'' Lady Caithness' mother, Molly Coke, 69, said: ''She was the opposite of being depressive.'' But Dr Goves told the inquest Lady Caithness had threatened to shoot herself in the past over the affair, which had become quite well known at Westminster. He had pleaded with Lord Caithness to keep the gun out of her reach but the earl said she had wanted him to leave it in the country house ''for her security'' while he was in London on parliamentary business.