The majority of CT scans require the use of a " contrast medium" to aid imaging. In your mothers case, the CT scanning would be looking at 2 areas;
1. Structural imaging, reflecting the brain anatomy, and is recommended as a routine procedure to exclude reversible causes of dementia
2. Functional imaging - assessing cerebral blood flow and cell metabolism., again to exclude reversible causes of dementia.
In neither of these specific circumstances is contrast medium required, so I think it less likely that your mum would need an injection. Can't absolutely rule it out though, siince i don't know the exact health circumstances of your mum.
Quite a nice general article on the procedure for a CT scan is on the Cancer UK website - I have included a link;
http://www.cancerhelp.org.uk/help/default.asp?page=148