The wife of British Iraqi-born engineer Saad al-Hilli, who was murdered with his family in the French Alps, had a "secret" American husband who died of a heart attack on the same day as the deadly attack, it emerged on Tuesday.

The revelation by French investigators adds a new twist to the murder mystery, which has thrown up a series of false leads since Hilli, his wife, Iqbal, and mother-in-law, Suhaila-al-Allaf, were shot dead along with a passing cyclist. Hilli's two daughters survived the attack at a layby on a wooded mountain road near Annecy on 5 September 2012.

"We have found out some surprising things about Iqbal, and we still don't have answers to some of the questions," said lead investigator Lieutenant-Colonel Benoit Vinnemann. Before marrying Hilli, Iqbal had never told her family about a US visit between February 1999 and December 2000 in which she married a dentist who was 13 years her senior. They divorced soon afterwards. Iqbal was herself a dentist. She met her second husband in Dubai a couple of years later.

The former husband, known only as James T, died on September 5 2012 in Natchez, Mississippi. The official cause of death was a heart attack.

"Is there a family secret that we haven't found? Does it concern Saad, or his wife Iqbal?" said Vinnemann.

In a further twist, the Annecy prosecutor, Eric Maillaud, said on Monday that a 35-year-old Iraqi had been placed under investigation last month on suspicion of carrying out a contract killing against Iraqis. However the man, who was not identified, had been released.

"He denied taking part in any contract whatsoever. He even denies the existence of this contract," Maillaud said. He added that investigators had been unable to establish any link with the Hilli family.

The Iraqi was the third person to be arrested in connection with the murders. Hilli's brother Zaid al-Hilli was arrested by British police who suspected a possible dispute with Saad over a family inheritance. However, he strongly denied any role in the murders and was subsequently released.

Then last February, French police appeared to have made a breakthrough by announcing the arrest of a 48-year-old Frenchman suspected of being the motorcyclist who had been spotted near the scene of the shootings. But he too was released although he continued to be questioned on unrelated arms possession offences.

The police have been puzzled by the weapon used in the shooting, which would appear to rule out a professional killing: a 7.65mm Lugar PO6 handgun, issued to the Swiss army and police in the 1920s and 1930s.

Hilli was staying in a caravan site in Annecy with his family when they decided to go on the fatal excursion to the village of Chevaline. One of his daughters was seriously hurt in the attack, while the other survived by hiding under the skirt of Iqbal al-Hilli, who was sitting in the back. The bodies were discovered by a British cyclist, Brett Martin.