On a cold winter night, three armed men disguised as police officers arrived at a suburban home in a small Canadian resort town and knocked on the door, claiming that they had an arrest warrant for a 37-year-old woman who was staying there.

After overpowering the homeowner, they seized the woman, Iranian-born Elnaz Hajtamiri, hauled her barefoot through the snow into a vehicle, and sped off into the dark.

Nearly three months later, police admit they are no closer to locating Hajtamiri, in a case that has baffled investigators.

“I have never, never come across a case like this,” Ontario provincial police detective inspector Martin Graham told reporters this week, adding that investigators had not determined a motive or received any ransom demands. They also have not located the white Lexus SUV vehicle used in the abduction on 12 January, nor have they identified its owner.

“My biggest hope is that Elnaz is alive,” said Graham. “My greatest fear is that she is not.”

Police took the “extraordinary” step of reaching out to the Iranian community in Toronto and Montreal as they expand the scope of their search, and are contemplating the possibility that she has been taken out of the country. This week, investigators also said they believed a brutal assault on Hajtamiri in December was linked to her abduction.

Two weeks before the kidnapping, Hajtamiri was attacked in the parking garage of her condo in Richmond Hill, a city north of Toronto. The assailants beat her with a frying pan and left her with serious head wounds that required 40 stitches. Police say they later retrieved a tracking device. Two other tracking devices were found in her car when she brought the vehicle in for servicing in November.

After the December attack, Hajtamiri feared for her safety and moved in with family in the town of Wasaga Beach, 145km (90 miles) north of Toronto. The only time she reportedly left the beachfront community was 10 January, to retrieve her vehicle, computer and mobile phone from police. Two days later, she was abducted.

On Thursday, York Region police announced the arrest of Riyasat Singh in connection with the assault at the parking garage. Singh, 23, faces four charges, including attempted kidnapping and attempted murder. Police also issued a Canada-wide warrant for the arrest of Harshdeep Binner, who faces the same charges.

Police say they do not believe the same men were involved in the kidnapping on January 12.

“We have at least five different people responsible directly for these crimes,” said Graham. “Despite the number of people involved, we have received no information that would provide us with a definite link as to where the investigation should be headed.”

In late January, police arrested her former boyfriend Mohamad Lilo, charging him with criminal harassment. The two broke up in October, but he tried to contact her the next month and police become involved. Officers would not say if he is a suspect in her abduction, but said they are investigating the relationship, which they said was both personal and professional.

Hajtamiri, who also goes by the surname Tamiri, emigrated to Canada less than four years ago, after she lost her husband. She had recently started her own cake-making company after leaving an import-export business.

In their latest push for new information, police released a video of Fariba Hajtamiri, Elnaz’s mother, pleading for her daughter’s release. Fariba, who still lives in Iran, said the family’s life has become “desperate” as they hope for Elnaz’s release.

“We desperately need your help,” she said in Farsi. “I beg you as a mother to guide us and tell us anything you know. Please, I beg of you.”