Another bombshell in the case of Savannah Guthrie's missing mother ... police tell TMZ Nancy Guthrie was taken by force from her Arizona home in the middle of the might.

A rep for the Pima County Sheriff's Office says Guthrie is believed to have been abducted from her home in the ritzy neighborhood of Catalina Foothills. The rep said investigators are looking at registered sex offenders in the area while combing through videos from cameras at Guthrie's home, neighbors' residences, local businesses and traffic lights.

Police declined to say whether blood was found inside the home, if the home was in disarray from a struggle or if there was forced entry.  But, the sheriff's department said they're talking with the Federal Bureau of Investigation, which has a long history working kidnapping and missing persons cases.

The sheriff's spokesperson tells us ... Customs and Border Protection are also involved in the case because the agency's specially trained K-9 dogs were used to help search for Guthrie. Police have not identified a suspect.

As we reported ... 84-year-old Nancy was reported missing Sunday afternoon, and was last seen Saturday night at her Tucson house. Authorities previously announced homicide detectives were investigating the case.

In a statement Sunday, Savannah said ... "On behalf of our family, I want to thank everyone for the thoughts, prayers and messages of support. Right now, our focus remains on the safe return of our dear mom."