Sorry for your loss.
Threshold question is whose trust is this and what is your relationship to it?
If this was your father's revocable trust that he funded while he was alive, then he is the grantor/former trustee and the trust became irrevocable on his passing and you became successor trustee (i.e. you're not the grantor in that scenario).
There should be no tax liability for you, your siblings, or the trust if you're just distributing corpus....the principal of the trust. If there are interest, dividends, capital gains or other income, then there may be tax liability when those income items are distributed.
