Authorities in Florida said Wednesday they had arrested the ex-husband of a missing woman on charges of second-degree murder and child neglect.

Steven Williams, 30, is being held at the Martin County Jail without bond, according to WFLX-TV. Martin County Sheriff William Snyder said Williams confessed to killing Tricia Todd in April and disposing of her body in a wooded area near Jonathan Dickinson State Park.

Officials are searching a 15-mile area for Todd’s body. Her body hasn’t been found and Williams failed to disclose how she died. Snyder said officials are redoubling their efforts to find her remains.

Todd, of Hobe Sound, was last seen at a Publix supermarket on April 26 and was reported missing the next day. Officials said she died the night of her disappearance. Her purse was found in her car and her keys were in the ignition, but her wallet and cellphone were missing.

"These two people were divorced. There were known issues about money," Snyder said.

Snyder said Todd’s 2-year-old daughter is now living with family members. Williams told authorities that there were no accomplices in Todd’s murder.

Williams agreed to submit a polygraph test on May 3 and nothing stood out that linked Williams to Todd’s disappearance, the sheriff’s office said.

“This obviously comes as a shock to all, but the family has expressed their appreciation for the Martin County Sheriff’s Office and all that they’ve done. They’ve commented on the community support and all the search efforts," Wesley Holden, a representative for the Todd family said in a statement.

"We’re just obviously very disappointed that Tricia’s not coming home alive, but they’re doing OK under all the circumstances."

Todd was an Air Force veteran and registered hospice nurse.

Williams served in the Air Force and returned to Florida from North Carolina, where he was stationed, last month, according to the Palm Beach Post. The Air Force said in a statement Wednesday they are “cooperating fully with civil authorities in this case.”

The Associated Press contributed to this report.

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