All wills need to be filed with the Probate Court, even if they are not probated. If there any assets in the persons estate (that were not in the trust) the will may still need to be probated so that those assets can be distributed according to the Will. You may want to engage an attorney for an initial consultation to make sure that all of the papers concerning the house are in order and that you are now the legal owner.
If there are no assets in the deceased's name then nothing needs to go through the probate process. If there are any assets in the deceased's name alone you need to probate the will. You also want to be sure that there is nothing in the deceased's name. Often, items are discovered many weeks after death in which case it's a good idea to file the will with the clerk's office.
Please be advised that the foregoing discussion is a generalized and hypothetical answer based upon incomplete facts and is not intended to serve as legal advice to you, nor should you regard it as an attorney-client communication or as creating an attorney-client relationship. If you desire legal advice concerning the situation you have described you should contact an attorney who has substantive experience in the fields pertaining to your question.
Yes, all wills must be probated.
Property in a living trust is not generally considered to be part of the probatable estate, however, so the house you were given via trust would most likely not be listed on the probate inventory. This is not something you have to worry about unless you are the executor or administrator of the estate.
Depending upon the specific circumstances, however, the house *may* be part of the estate's taxable assets for both federal and state estate tax purposes.
You ask, "do I still need to do anything after he dies?" Are you the executor or the administrator of the estate? If so, yes, you have plenty to do, and I recommend that you consult with an attorney who can help you determine your rights and responsibilities under the specific facts and circumstances.
Beacon Hill Law
(((DISCLAIMER: The above should not be taken as legal advice nor the formation or creation of an attorney-client relationship. It is provided for general informational/entertainment purposes only.)))