Even if they were in a solid state of mind during the crime itself, that does not mean that they automatically will be when the trial comes. If the trial comes and the person is not competent and/or able to assist in their own defense, there is a good chance that the trial will be delayed until the person can be treated and thus be able to assist in their own defense or it's also a possibility that such competence will never be present and the alleged offender would have to be treated as such. The second person would not be competent because they have to be able to have the lucidity and self-awareness to answer questions and know what is going on during the trial. After all, if they are innocent yet they are not lucid, they would potentially be convicted when they should not be because they can end up doing or saying things...

Even so, a properly trained forensic psychologist or other related professional that is doing their job and doing it well can clearly ascertain whether the person is competent or not based on federal or any other applicable jurisdictions such as state, city and/or county.
References

Hare, R.D. (1996). Psychopathy: A clinical construct whose time has come. Criminal Justice and Behavior, 23(1), 25 -- 54.