Lt. Mike Horn said the charges stem from Smith's repeated and apparently desperate attempts to adopt 8-month-old Gabriel Johnson, not from the boy's Dec. 26 disappearance in San Antonio, Texas.
"I am innocent, and God is with me," a handcuffed Smith told television reporters as she was taken in for booking.
Tammi and Jack Smith, of Scottsdale, Ariz., had been considered "persons of interest" for weeks in the investigation of the disappearance, but Horn said that's no longer the case.
"The only thing I can surmise here is that the authorities think she knows something that she hasn't told them," Tammi Smith's lawyer, Michael Kimerer, told reporters.
Horn said all of his agency's leads into the disappearance have been turned over to San Antonio police, who are conducting their own investigation.
Speculation continues that San Antonio authorities will search a landfill for the boy's body. Managers of a landfill there have blocked off an area that might be searched for the baby, but police said they hadn't yet searched the site and decline to say whether they plan to do so.
Jack Smith told The Associated Press Tuesday that police crossed the line by arresting his wife and trumped up charges against her.
"It's clear that we had nothing to do with this, and why they're trying to make a case against my wife, I don't know," he said. "We have done nothing wrong."
Police say Gabriel's mother, 23-year-old Elizabeth Johnson, drove Gabriel to San Antonio from Tempe, stayed about a week, then took a bus to Florida without him. She was arrested Dec. 30 in Florida and is charged in Arizona with kidnapping, child abuse and custodial interference.
She has refused to say where the baby is, but told Gabriel's father she killed him and threw his body in a trash bin. She also has said she gave the baby away to a couple in San Antonio, but police said she was vague in describing who they were.
The Smiths had sought to adopt Gabriel from Johnson, who gave the couple temporary guardianship over him for about 10 days in December before she picked him up and left Arizona.
Tammi Smith told co-anchor Maggie Rodriguez she and her husband don't have any idea about Gabriel's whereabouts. "I sure wish we did. I sure wish (Elizabeth Johnson) told us any name, any -- of anything," Smith said.
"We spent ten years building a successful business here (in Scottsdale)," Jack Smith said, "and, for us to throw that away, or even the thoughts of throwing that away for someone we had known for nine days, that's ludicrous. No, absolutely not."
"Technically," Tammi Smith told Rodriguez at the time, "it seemed as if she wanted the best for him (Gabriel), and knew she could not give that to him herself."
In a Tuesday court document detailing the charges against Tammi Smith, police describe for the first time the lengths to which she went to adopt Gabriel.
Before Johnson left Arizona with Gabriel, those efforts included repeated phone calls and text messages to his father, Logan McQueary, pressuring him to relinquish his parental rights to the Smiths, according to the probable-cause statement.
Horn said Smith also tried to recruit male acquaintances to get them to put their name on a document seeking to have McQueary submit to a DNA test. The document required the name of a potential father, and when Smith couldn't get anyone to agree to it, she forged her cousin's name, Horn said.
After Johnson and Gabriel left the state, Smith sent a text message Dec. 27 to McQueary asking him if they could meet the following day, according to the document.
"I'm afraid she'll be gone forever, cause she doesn't want to go to jail for kidnapping," she wrote. "The only way she'll come back is if my attorney faxes the signed papers to her so she won't get in trouble, and Gabriel b w/us."
Smith also tried to change court jurisdiction over Gabriel to Tennessee in an apparent last-minute plan to get Johnson to take the boy there and adopt him out without needing McQueary's approval, thus clearing the way for the Smiths, Horn said.
And on Jan. 4, Smith suggested in a voicemail to the judge in the boy's custody case that he give the Smiths guardianship because Johnson wouldn't return to Arizona with him unless she knew he would be "safe," according to the document.
Police say Smith told them to what other lengths she would go to get Gabriel.
"Tammi Smith stated she was going to use her attorney's help to pressure Logan to pay previous child support, current child support and be responsible for visitation," according to the document. "Tammi stated due to the above listed pressure the hope was that Logan would release his custodial rights and the adoption could proceed."
Jack Smith said his wife wrote down her cousin's name on a court document for a paternity test "as a joke" and because she was rushed by a court employee.
"We didn't think it was a big deal," he said.