Does Appellant in a civil case need to serve Respondent with the record on appeal? What Rule of Court is applicable?

If appellant opted to use an appellant's appendix then you must be served with it. On the other hand, if appellant opted to use a CT, you are responsible for obtaining your own copy. Same with the RT. Under certain circumstances you may borrow appellant's copies. See Rule 8.153, which you can access online.

I assume that this is an appeal in an unlimited civil case to the Court of Appeal. Rule 8.153. Lending the record (a) Request Within 20 days after the record is filed in the reviewing court, a party that has not purchased its own copy of the record may request another party, in writing, to lend it that party's copy of the record. The other party must then lend its copy of the record when it serves its brief. (b) Time to return The borrowing party must return the copy of the record when it serves its brief or the time to file its brief has expired. (c) Cost The borrowing party must bear the cost of sending the copy of the record to and from the borrowing party.