The dye used for CT scans is safe for most people.
The dye that is used for CT scans is iodine based and as long as the patient has no other health issues such as kidney issues, bladder issues etc then the Iodine based dye used for CT scans should pose no health issue.
I've had the dye for CT scans put into myself before for a CT scan a few different times and nothing bad has happened to me.
There are some risk though but for most people who go in for a CT scan can safely have the dye put into them without any issues.
The doctor should let you know all the risks associated with the dye that is used for CT scans but if you don't have kidney disease or other kidney problems etc then it's usually safe to have the CT scans done with the dye put inside you.