A visitor to Knutsford said they were covered in pigeon droppings.
"They not only look a mess, but it's also a health hazard," said the woman.
But yesterday (Tuesday) Crown Court spokesman Mark White insisted the steps were cleaned regularly.
"The exterior of the building and its grounds are maintained by an external contractor," he said. "And they clean the area every month or so."
He added that the court rooms were cleaned daily.
"I haven't received any complaints about the state of the steps and the staff who visit the courts have not noticed a problem," said Mr White.
But he promised that his security staff would check the area.
"That way we can check the extent of the problem so that appropriate action can be taken," he said.
The imposing court house, which is not in session until next month, is one of Knutsford's best known landmarks.
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