Roman Catholic Marriage Tribunals adjudicate the validity of marriages under the canon law of the Catholic Church. These courts sometimes use psychologists when making their decisions.
One ground for finding a marriage invalid is Canon 1095, which states a person is incapable of marriage if they "suffer from a grave defect of discretion of judgment concerning the essential matrimonial rights and duties," or they "are not able to assume the essential obligations of marriage for causes of a psychic nature." There are similar requirements under civil law as well, of course.
There are thousands of such cases in the US decided every year, though it is unclear what percentage of those cases call for the use of a psychologist. What is clear is that there are no consistent method for conducting such an assessment. One recent study suggests that a uniform battery of assessments and standardized procedures would be valuable.