Superior Court Commissioner Maren E. Nelson said the question is whether the actor is attempting to turn the couple's child against Basinger.
"Whether that is taking place or not, I cannot determine," Nelson said. "Someone, an evaluator, needs to spend time with Ireland and the parents to work on that issue."
Neither actor attended Friday's court hearing.
Baldwin was given a week to accept the court-appointed psychologist or the judge said she would select another one.
In October, Basinger's attorney said Baldwin suffered from "severe emotional problems" and that he had been accused of domestic violence in the past.
Baldwin, 48, countered in court documents that the 52-year-old Basinger "has a pathological need" to turn their daughter against him. He also sought a psychological evaluation and parenting classes for Basinger.
The acting duo married Aug. 19, 1993. They separated in 2000 and divorced in 2002.