How to get Constance to calm down in Skyrim
From the elder scroll wiki :
Whether she saw the murder of Grelod or not, Constance will remain in a state of panic from Grelod's death until Innocence Lost is completed by talking to Aventus Aretino. However, she will not acknowledge the Dragonborn as the murderer once this questline is completed.
Complete the Innocence Lost quest (by talking to Aventus in Windhelm) and she will be back to normal.