Civil is a type of case.
There are 3 main types of court case - civil, criminal & family law.
There are 4 main jurisdictions - District, Circuit, High/Central Criminal & Supreme which all hear these 3 main types of case (depending on the importance of the issues etc.).
There is no such thing as a "civil court", however, there could be a judgement on a civil case in either the District, Circuit, High or Supreme Court. You need to find out what jurisdiction the case was decided in and then check with the relevant court office.