Hi Kristine,
Most likely, there are several objects that match the same mapping criteria in the projects you mentioned. So, TestComplete uses the first found object that matches the mapping criteria, and this is not the check box that was found in Project A. That's why, the found object may not contain the ClickItem method.
So, to resolve the problem, please configure the name mapping scheme in all other projects in the same way as it is configured in Project A. For more information, please refer to the Name Mapping - Overview help topic.
