All humans learn rules of social etiquette. Moreover, we judge others based on how well they conform to these rules. The presence of a character in your interface makes rules of etiquette directly applicable to your design.
We expect reciprocity in our interaction and when it doesn't happen we tend to view the behavior as incompetent or offensive. In new or formal situations, politeness is usually expected. Only after a relationship is established does familiarity allow for less formal interaction. So when in doubt, be polite.
For example, consider the appropriate protocol for starting and ending a social interaction. When engaging in a new social context, we generally greet each other and indicate our intent to leave before we depart. You can apply this model directly to character interaction; avoid the character appearing or disappearing without an appropriate indication.
A part of politeness is how we respond. We expect responses that are appropriate. For example, if you ask, "What day is it?" you don't expect the response to be "10 apples." However, accuracy and relevance are not enough; you may also need to determine the context. An accurate response could be "Monday" or "August 25th." Similarly, the wording of a response can be accurate but still be offensive, depending on intonation, facial expression, or other non-verbal behaviors.
In addition, we address each other while talking: we face the person, turning only to direct attention to something. Turning one's back, without some purpose, implies disinterest and is generally considered to be impolite.
Politeness also affects the way we respond to or perceive others. For example, social research indicates that we are more likely to be honest about our evaluation of others when asked by another person than when the people ask about themselves. Similarly, we accept positive evaluations of others more readily than positive self-evaluations. Immodest behavior is generally considered impolite. Therefore, unless intentionally trying to promote an impolite personality style, avoid having the character compliment its own performance.
Also consider the cultural impact on social etiquette. This may apply to the character's attire, gestures, or word choice. While polite behaviors may vary by culture, the concept of politeness is cross-cultural.