(CNN) A Connecticut physical therapist under investigation for alleged health care fraud killed his wife and three children at their home in Florida, deaths that were discovered only when federal agents tried to arrest him in the fraud case, authorities say.

The four may have been dead for around a couple weeks, perhaps undetected by a sheriff's deputy who did a well-being check at a relative's request in late December but found no cause to enter the home, Osceola County Sheriff Russell Gibson said.

Anthony Todt, 44, is being held in a Florida jail on suspicion of killing Megan Todt, 42, their three children, ages 4, 11 and 13, and the family dog, Gibson announced at a news conference Wednesday.

Todt initially was detained Monday at his home in Celebration, a community adjacent to Disney World, by federal agents and sheriff's deputies serving a federal arrest warrant in the health care probe.

Deputies checking the home found the four bodies. Todt confessed to killing them, and investigators believe it happened sometime at the end of December, Gibson said, citing Todt's statements to them.

Gibson said he didn't immediately know why Todt allegedly killed his family and the dog, and he declined to say how they were killed, saying a medical examiner has yet to make a final ruling.

"Myself, I cannot understand what would cause a person to commit such evil and horrendous acts," Gibson said.

Investigators still need to confirm the identities of the four people, but they "strongly believe" they are Megan and her children, based on Todt's confession, Gibson said.

Todt was taken to a hospital after telling the officers Monday he took some pills. The hospital eventually released him, and he was arrested Wednesday on suspicion of homicide and animal cruelty, Gibson said.

It was not clear whether Todt has an attorney. He has an initial court appearance set for Thursday.

As detectives escorted him from the sheriff's office to a vehicle for transport to jail Wednesday, Todt declined to answer questions from reporters about the charges against him.

Todt's sister, Chrissy Caplet, released a statement: "Tony and Megan were devoted loving parents who loved their children and (their dog) Breezy every day and were so involved in their community. The families of Tony and Megan ask for privacy during this difficult time in our lives as we mourn the loss of our families."

Detectives escort Todt to a vehicle for transport to jail on Wednesday.

Todt accused of Medicaid and insurance fraud

Shortly before Todt is alleged to have killed his family, a federal investigation into his Connecticut physical therapy business was picking up steam, court documents show.

Todt ran the business out of two locations in Colchester, Connecticut, but spent weekends at the Florida home, where his family lived, authorities said.

The Department of Health and Human Services was investigating Todt's business over suspicions that he was billing Medicaid and private insurance for services that he had not provided to patients, according to an affidavit filed in federal court in Hartford.

Federal agents raided the two offices on November 21 and interviewed Todt, who admitted to fraudulently billing insurers, an investigator alleged in the documents.

"When specifically asked if he routinely billed for services that he didn't provide, Todt replied, 'Yes,' Todt elaborated that he started 'adding stuff' when he performed the billing and randomly chose the patients that he submitted extra claims for payment for," according to the affidavit.

Todt told investigators he did this to keep pace with personal loans he'd taken out, and when asked if he was living above his means, he replied, "That's the best way to put it," according to the document.

Todt said neither his wife nor his employees knew of his billing practices, according to the affidavit.

The bodies were found Monday at a home in Celebration, Florida, a community adjacent to Disney World.

One of Todt's relatives asked for a well-being check in December, authorities say

Todt said he wanted to plead guilty, and the investigators ended the interview and asked him to have an attorney contact them as soon as possible, according to the affidavit.

But no attorney contacted them in November and December, the affidavit says.

After the November interview, two of Todt's employees told agents that Todt claimed he'd be back in Connecticut to treat patients, but he never did. Eventually payments to Todt's employees stopped, and both Colchester offices closed, the affidavit said.

On December 29, one of Todt's out-of-state relatives asked the sheriff's office in Florida's Osceola County to check on the family, "because she had been told that (the Todt family) all had the flu and she had not heard from them in two days," Gibson said.

A deputy went to the home, but no one answered the door. The deputy did not enter the house, because he or she had no cause to do so, the sheriff said.

"The deputy walked around the house, checked with neighbors. The blinds of the home was closed. Nothing suspicious was noted, and therefore they didn't enter the home," Gibson said.

In hindsight, it is possible that the killings had happened by then, the sheriff said.

Deputies returned to the home on January 9, this time because federal agents had told the sheriff's office that Todt was under investigation, Gibson said.

"Deputies from that point made several attempts to make contact with Anthony and the family over this past weekend," but didn't find Todt there until Monday, Gibson said.