The neurological test was a medical test used for determining if the functioning of the nervous system was impaired.
In 2256, neurological tests of the tardigrade Ripper by medical staff aboard the USS Discovery indicated that the animal might be sentient. (DIS: "Choose Your Pain")
In 3189, the medical staff of the Discovery conducted neurological tests on Lieutenant Keyla Detmer, who suffered a head injury when the starship was crash landing on a planet. As Doctor Tracy Pollard cleaned Detmer's bruise with a protoplaser, the physician informed her that the tests were clear and there was no concussion. (DIS: "Far From Home")