An investigation in the spiritual sense suggests that concepts, precepts and beliefs need to be very carefully looked at.
Psychological / emotional perspective: Many people do not like to look too closely at their own emotions, but to be investigating a building, for instance, can suggest that we are trying to understand ourselves and our own reactions.
Material aspects: When we are unsure of our own position within a work hierarchy or family structure we may dream of an investigation in order to feel comfortable.
If we are being investigated in dreams we may feel we have not fulfilled a task to our own satisfaction. Such a dream may also suggest that we are being too closely monitored for our own liking.