From Connecticut Statute Sec. 12-704c (h):
"Property tax” means the amount of property tax exclusive of any interest, fees or charges thereon for which a taxpayer is liable, or in the case of any husband and wife who file a return under the federal income tax for such taxable year as married individuals filing a joint return, for which the husband or wife or both are liable, to a Connecticut political subdivision on the taxpayer's primary residence or motor vehicles;... "
https://www.cga.ct.gov/current/pub/chap_229.htm#sec_12-704c
Presumably, since you do not own the property, you are not liable for the tax. Thus you are not eligible to take the credit.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.