Police have determined that Kamille “Cupcake” McKinney -- a 3-year-old girl kidnapped from a birthday party in Birmingham, Ala., whose remains were later found in a dumpster -- died by asphyxiation, or suffocation, according to court warrants read by a judge Friday.

Patrick Devone Stallworth, 39, and Derick Irisha Brown, 29, made their first court appearances after the Jefferson County District Attorney charged them each with capital murder on Thursday.

They are accused of snatching the child from an outdoor birthday party on Oct. 12 around 8:30 p.m. at the Tom Brown Village housing community and later dumping her body in a trash bin close to where the suspects lived.

Kamille's body was found on Oct. 22 after a 10-day search.

Birmingham police arrested Stallworth and Brown the day after McKinney went missing and impounded a Toyota SUV after authorities said Stallworth was identified as the man seen in surveillance footage at a nearby store around the time of the child's abduction.

Police said there is no connection between Stallworth, Brown and McKinney's family.

Jefferson County Circuit Judge Clyde Jones read both Stallworth and Brown’s capital murder warrants at their initial court appearance on Friday.

Stallworth told the judge: “I don’t understand why I was charged with [the] murder of this child,” when asked if he had any questions about the warrant, according to a local Birmingham news report.

The judge told Stallworth that his lawyer would explain the charges to him and that the state will present evidence against him at a preliminary hearing if he chooses to have one, but Stallworth said he plans to hire his own attorney within the week.

Brown was appointed attorneys from the Jefferson County Public Defender’s Office to represent her in the capital murder case; they were already representing her in an unrelated matter.

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The two are being held without bond at the Jefferson County Jail and could face the death penalty if convicted.

McKinney's father said his daughter was fondly regarded as Cupcake because "when she came out, she was all cute and red with little brown eyes and I said, ‘That’s my cupcake.’”

A Celebration of Life ceremony for McKinney is scheduled for Sunday, followed by visitation and burial.

Fox News' Morgan Phillips contributed to this report.