SARASOTA, Fla. -- The father of Carlie Brucia said he thinks police "acted responsibly" in the search for his daughter.

The 11-year-old Florida girl was found dead last week, several days after a security camera captured her abduction. Joseph Smith, 37, remains in custody. Police believe he's the man seen leading the girl away on the videotape.

CARLIE BRUCIA Video: Dad: Police Acted Responsibly Video: Sheriff Announces Carlie's Death Video: Girl's Abduction Caught On Tape Video: Mother Makes Plea For Daughter's Return Discussion: Kidnapped Florida Girl

Joe Brucia told reporters Monday that he doesn't agree with critics who said police should have started an Amber Alert for his daughter. He said he doesn't think it would have helped -- and that if it's used too many times, people won't take it seriously.

An Amber Alert is a way of alerting the public to new child kidnapping cases.

Brucia also said he thinks a fund being established in response to the tragedy shouldn't be named the Brucia Family Fund. He said the fund isn't really for the family, and that if possible, he'd like to rename it the Carlie Brucia Rescue Fund. He said he thinks that would make his daughter happy.

Meanwhile, the videotaped abduction is prompting questions about Florida's justice system.

Smith, the man accused of killing Carlie Brucia, has a lengthy criminal record, but spent relatively little time behind bars.

Police filed first-degree murder and kidnapping charges against Smith, who had been on probation for the better part of the last decade -- with at least 13 arrests in Florida since 1993.

Smith is an unemployed mechanic. His convictions include assault against a woman, weapons charges, drug possession and numerous fraud counts. He was arrested in 1997 on kidnapping and false imprisonment charges -- but was acquitted a year later. Despite more than a dozen convictions, the longest time Smith served in prison was less than 14 months.

Brucia's father is demanding answers and wants Gov. Jeb Bush to launch an investigation.

Florida Attorney General Charlie Crist said his office is already reviewing whether the state's probation laws should be toughened.

Friend: Car Showed Signs Of Struggle

A close friend of Smith said a struggle may have taken place in the back seat of a station wagon that police believe was used in Brucia's abduction.

Ed Dinyes said Smith borrowed the car from a friend about the time Carlie went missing on Super Bowl Sunday. He said when the car was returned, the back seat was in disarray, and the car had 300 extra miles on the odometer, and scuff marks on the back of the seats and on the window.

Carlie's body was found early Friday behind a Sarasota church. Sheriff's deputies have not said how she died.

Investigators believe Smith was the man captured on security cameras at a Sarasota car wash grabbing the sixth-grader's arm and marching her away.

The cameras also caught the borrowed 1992 Buick station wagon passing by in the car wash parking lot.