“Cette nuit” alone is ambiguous, just like “cette semaine” is ambiguous when used during the weekend (it can mean last week or next week).

As often in such situation, the context should give a hint to make the term unequivocal:

• “Cette nuit il a plu” -> It rained last night
• “Cette nuit il pleuvra” -> It is going to rain tonight

Also, I would say that the later it is in the day, the more likely “cette nuit” means tonight.