You can search the case on ecourts website with help of name and from there you can get the case number.
http://ecourts.gov.in/tn
Party search link chennai
http://services.ecourts.gov.in/ecourtindia/cases/ki_petres.php?state=D&state_cd=10&dist_cd=13
Select family court in this type name and year of filing .
When you get the case number by that you can apply.for.certofied copy of the decree and order can keep that for your record.