Not sure what the problem is here, but two possibilities spring to mind
1. You have not granted the person you want to assing it to the permission "assignable user" - check the permissions scheme for the project
2. You are not able to see the list of users. See global permissions in the admin section and check you have the right to "browse users" in there. If you don't have it, you will not see lists of users and autocomplete in user fileds will not happen.
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