Tabata, who spent part of spring training with the Pirates, did not take part in workouts at their minor league complex Wednesday and declined to talk to reporters.
"I was shocked to be told that my wife was arrested for kidnapping," Tabata said in a statement issued by the team. "I am hurt, frustrated and confused by her actions. I have and will continue to cooperate with law enforcement officials in any way that I can. Until I have all of the facts, I cannot comment any further."
The Pirates also said they could not further discuss the incident.
"Due to the nature of this ongoing investigation, we cannot discuss any specifics of the case, other than to say that, like Jose, we are extremely thankful the young child was safely returned to her family," Coonelly said. "Our hearts go out to her and her family for the pain they must have endured during the hours that she was missing."
The incident probably won't keep Tabata off the field for an extended period. He is expected to begin the season with Double-A Altoona of the Eastern League, where he was optioned last week after hitting .407 in 27 exhibition at-bats with the Pirates.
"We continue to be enthusiastic about Jose Tabata as a person, player and member of the Pirates' family," general manager Neal Huntington said. "Jose will return to the field in the coming days when he and we feel the timing is right. Jose has been a pleasure for our staff to work with and we will continue to work closely with him with respect to his development and growth in all areas."
The infant, Sandra Cruz-Francisco, was taken from her mother, Rosa Sirilo-Francisco, about 3 p.m. Monday by a woman her family only knew as "Janet," according to police in Plant City, about 60 miles from Bradenton. The mother had taken her baby for a checkup at the Plant City Health Department, where she met Janet, who said she was an immigration official. The woman told Sirilo-Francisco there were officers at her home waiting to deport her and the child's father to Mexico.
The woman known as Janet offered to help, but said she had to take the baby. The two women drove with the infant to a farm where the child's father works and Janet told him the same story, and the mother later handed the child over.
Authorities in Manatee County said Pereira was detained after an anonymous tipster called police to report a woman in downtown Bradenton had information about the missing baby. The baby was handed over when police responded to that call.
Tabata was considered one of the New York Yankees' top prospects last year, only to walk out of a game involving their Double-A Trenton farm club early last season. Tabata apparently was frustrated by his slow start.
The incident partly led to the Yankees including Tabata in the July trade in which the Pirates dealt outfielder Xavier Nady and left-hander Damaso Marte to New York for Tabata and right-handers Ross Ohlendorf, Jeff Karstens and Daniel McCutchen.
After the trade, Tabata hit .348 in 22 games with Altoona - or 100 points higher than he hit in 79 games for Trenton - and had three homers and 13 RBIs in 89 at-bats. Tabata, a native of Venezuela, also impressed the Pirates this spring with his line-drive power, throwing arm and ability to learn quickly.
Upon making the trade, the Pirates apparently were unaware that Tabata was married to a woman more than twice his age who, according to the St. Petersburg Times, spent more than two years in a state prison about 10 years ago for an arson case. Family members told the newspaper that Pereira, a native of Puerto Rico, has four children of her own, all of them teenagers or older.
The woman apparently has used at least four names in the past, and the name given to police does not match the one - Mayita - in the Pirates' media guide.
Tabata and the woman were married in January 2008 in Hillsborough County.