Going off of the info that LE doesn't believe the tape was used to stage a kidapping, I believe it was used to silence her before/during the murder. Since the remains have been found, most of LE's investigation has centered inside of the house--particularly Casey's room. IMO, they found fibers on the tape that show the bedroom to be a crimescene. The bedroom is probably where little Caylee's mouth was taped shut--perhaps even where she died.
<SNIP>
"...Investigators said they're still trying to determine why the child's mouth was taped shut with duct tape. At this point they said they do not believe this was meant to look like the child was killed by a kidnapper..."
http://www.wesh.com/news/18276452/detail.html
ETA: Depending on how close the reporter translated what LE actually had to say, the clue may be that LE is trying to determine "Why the child's mouth was taped shut with duct tape." Why would anyone need to "shut a child's mouth?"
<SNIP>
"...Investigators said they're still trying to determine why the child's mouth was taped shut with duct tape. At this point they said they do not believe this was meant to look like the child was killed by a kidnapper..."
http://www.wesh.com/news/18276452/detail.html
ETA: Depending on how close the reporter translated what LE actually had to say, the clue may be that LE is trying to determine "Why the child's mouth was taped shut with duct tape." Why would anyone need to "shut a child's mouth?"