Stephen Edward Palmer, 30, had pleaded guilty in the Supreme Court in Launceston this morning to ill-treating a child by wilfully neglecting to seek medical treatment.

Palmer was convicted of the crime and escaped jail, however if he reoffends in the next three years, he will be re-sentenced for this offence.

"It seems obvious the fractures were suffered by the baby by his (Palmer's) hands or those of his partner, but the evidence does not establish who," Chief Justice Ewan Crawford told the court during sentencing.

"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."

This morning, the court was told that Palmer called an ambulance for his daughter at 5.20am on December 22, 2010.

She was diagnosed at the Launceston General Hospital that morning with a spiral fracture to her upper left arm and two bucket fractures to her lower arm.

In an interview with police later that day, Palmer said he noticed her arm was swollen for two to three days earlier.

Prosecutor Peter Sheriff said it was not known how the injury occurred.

Palmer told police he had thought about throwing the baby on the bed, but hadn't, "because what if she bounces off and gets a concussion.''

Defence counsel Adrian Hall said if Palmer had not admitted neglect by failing to seek medical treatment straight away, the case against him may have resolved in the same way as the charge against his then partner, and the baby's mother, Kylie Parker.

The case against Ms Parker was thrown out yesterday because the judge instructed the jury to deliver a verdict of not guilty.

"He remains adamant that he did not cause the injury but fears that others would have a different view, and he did not want to lose the child,'' Mr Hall said.

Palmer will be sentenced at 4pm.