"To assign the case" means to choose or allocate a particular issue, situation, or legal matter to a specific person or team for investigation, handling, or resolution. Full definition
It may not have been assigned a case number at the time that the document was given to you but it almost certainly has a case number now. (law.stackexchange.com)
We will provide you with regular updates about your case, travel to meet with you, assign you a case manager and return phone calls about new cases within one business day. (justiceyoudeserve.com)
Following the initial training period, investigative assistants will continue to receive ongoing training and supervision from an experienced staff investigator who will serve as a mentor and will be responsible for assigning cases. (bds.org)