But child advocacy groups have criticised the outcome and said Tasmania's child protection laws should be strengthened.

Stephen Edward Palmer, 30, now of Scottsdale, was sentenced in the Supreme Court in Launceston yesterday after pleading guilty to ill-treating his two-month-old daughter, who had arrived at hospital with multiple arm fractures.

Chief Justice Ewan Crawford recorded a conviction but did not impose any other penalty.

Palmer had called an ambulance to his then home in Pioneer Parade, Ravenswood, at 5.22am on December 22, 2010, and told paramedics he had heard his daughter's arm crack while he was changing her nappy.

An X-ray taken at the Launceston General Hospital that morning showed the baby had a spiral fracture in her obviously swollen upper left arm and two chips from the bone in her left forearm.

Palmer later admitted to police he had noticed the swollen arm three days earlier and had neglected to seek medical assistance.

Chief Justice Crawford told the court he was obliged to sentence Palmer on the basis of neglect alone, but said that much was ``unknown concerning the true facts''.

``It seems obvious that the fractures were suffered by the baby by his hands or those of his partner, but the evidence does not establish who,'' Chief Justice Crawford said.

``If he was to be sentenced for intentionally injuring the child and causing the fractures, imprisonment would be the appropriate sentence.

``But the limited factual basis presented to the court does not justify that course.''

Palmer was not jailed but could be resentenced for this offence if he commits another crime punishable by imprisonment in the next three years.

The case against the child's mother and his former partner, Kylie Parker, was thrown out on Tuesday. Chief Justice Crawford said she had no case to answer and directed the jury to deliver a verdict of not guilty.

The baby and two older siblings live with their grandparents.

Bravehearts founder Hetty Johnston said the system had failed the baby.

``The laws and the system are broken - just as broken as that little girl's arm,'' Ms Johnston said.

``I've seen heavier sentences handed down for neglecting to take an animal to a vet.''

Ms Johnston praised the sentencing comments made by Chief Justice Crawford and said Tasmania's child protection legislation should be reformed to give the court greater scope to punish parents who neglect or abuse their children.