Meredith Katharine Borowiec pleaded not guilty to two charges of second-degree murder, but legal wrangling forced the judge to adjourn the matter until Tuesday morning.
Borowiec, who is 31, was initially charged with attempted murder after a baby boy was found crying in a garbage bin in October, 2010.
A few months later, police laid two second-degree murder charges against Borowiec.
Investigators have said they believe she gave birth in 2008 and again in 2009, and that both babies died soon after they were born.
Borowiec's trial in font of a judge without a jury is scheduled to last six weeks.
She faces a separate trial on the attempted murder charge in November.
The story of the baby found in the garbage was especially gripping because the infant's father played a part in the rescue, apparently not knowing the child was his.
The father, who told police he didn't know his girlfriend was pregnant, was on his way home when he and other passersby heard crying coming from the trash bin.
They jumped in and found the infant in a garbage bag.
Police and paramedics were called and the baby was taken to hospital.
The child has recovered and is healthy.
Borowiec remains in custody.
Note to readers: This story has been clarified. An earlier version did not make clear the attempted murder charge would be handled in a separate trial.
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