No - you will not be considered an AZ resident unless you actively try to change your residency to AZ (change driver's license, voters registration etc.)
The fact that you are being a kind grandchild and taking care of your grandmother will be considered only a temporary relocation even if it is for more than a year.
Therefore, you will remain a resident of CO, if that was your original state of residency before you went to take care of your grandmother.
