State child-welfare investigators first suspected something was wrong inside little Jillian Kalous’ home on April 24, 2012. That’s when the then-3-month-old girl was admitted to Sherman Hospital in Elgin with multiple broken bones.

The Illinois Department of Children and Family services investigated, determining that the infant and her brother both were at “substantial risk of abuse.” Officials later took the children from their parents, records show.

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But that summer, a Kane County judge decided that Jillian and her brother Bradley should be returned to Kevin and Jaclyn Kalous, who were raising them in a well-kept split level in a quiet neighborhood on Elgin’s northwest side.

Then — two days before what would have been Jillian’s first Halloween — paramedics were called and rushed Jillian back to Sherman.

Doctors there noted “massive brain swelling and visible bruising on both inner thighs” and transferred her to Lutheran General Hospital in Park Ridge. She died there on Nov. 2, 2012.

The Cook County medical examiner ruled the case a homicide, finding that the 9-month-old “died of blunt head trauma due to child abuse.”

Now, more than a year later, the Elgin police are still investigating her death — and the Kalous family says the medical examiner’s conclusion is wrong.

The case underscores the difficulties involved in removing children from their families after an allegation of abuse or neglect.

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DCFS took that dramatic step with the Kalous family after the first report of abuse in the household. Attempts to reach Kane County’s chief judge about why Jillian and her brother were ordered returned to her parents were unsuccessful.

DCFS officials declined to comment on the case, citing juvenile confidentiality laws.

Speaking generally, outgoing DCFS director Richard Calica says the agency and the courts frequently are forced to make difficult decisions about whether to leave children in their homes.

“How do you decide which particular individual is likely to inflict a fatal injury on their child in the future?” Calica says. “We’re walking an interesting tightrope because we’re trying to protect children without harming them.

“When you take a kid away from their parent, you’re mutilating them psychologically… . So while we’re trying on the one hand to decide whether the parent is really going to hurt this kid or not, which is a very inexact science, we have the other problem of trying to ‘first do no harm.’ ”

Those decisions are at the heart of a rise over the past few years in the number of child abuse and neglect deaths statewide in which DCFS was investigating or monitoring the children and their families.

The number of those deaths more than doubled, from 15 in 2010 to 34 in 2011, and held steady at 34 last year despite the child-welfare system’s involvement, a Chicago Sun-Times and WBEZ examination of 10 years of neglect and abuse cases found.

DCFS now has once again removed Bradley Kalous from the custody of his parents, according to Kevin Kalous.

“They took him the day Jillian went to the hospital,” Kalous says, putting him with a grandparent. “We’re still waiting to determine what happens to our son.”

His attorney, Kent Dean, says: “There are ongoing proceedings in relation to this matter, and it would not be appropriate to comment other than to confirm that my clients have been cooperative at all turns and steadfastly deny causing harm to their child. They are exemplary people, and our medical experts have a very different interpretation, which contradicts what the Cook County medical examiner’s office stated.”

According to the medical examiner’s report, Kevin Kalous heard Jillian gagging and choking around 12:30 p.m. on Oct. 29, 2012, shortly after he’d given her baby formula and put her in her crib.

“Mr. Kalous went and reached for the subject, when the subject became unresponsive,” the report says. “When he heard the subject gagging and choking, he performed a finger swipe, with negative results.”

Kalous called the fire department and was performing CPR when his daughter vomited, according to the report, which says Jillian suffered from “multiple seizures” while being treated at Lutheran General before her Nov. 2 death.

Elgin police and the Kane County state’s attorney’s office won’t comment, citing the pending investigation.

Chris Fusco and Monifa Thomas are Sun-Times staff reporters. Tony Arnold is a reporter for WBEZ.