Hi, you certainly can ask the trustee for a copy and they may give it to you. However, if they don't want to it can be difficult to force them to. This is often cited as one of the advantages of a living trust and we discuss it at privacy of a living trust.
You'll see in that article that it is possible to petition a probate court to order a copy be given to you and there also are certain situations where a living trust can become public (i.e. if filed in county real estate or court records, etc).
So, short answer is yes, it's possible for you to get a copy of the living trust, but can be difficult.