Yes, you can bombard with artillery, and patrol over with planes without going to war.
Attacking unit of country A with rockets or by directly attacking with planes will lead to war with country B.
I'm sure this has been answered before but please bear with me 
If I am at war with Country A, and Country A has troops in Country B, but I am currently at Peace with Country B, can I hit Country A's troops with artillery without going to war with Country B?
Yes, you can bombard with artillery, and patrol over with planes without going to war.
Attacking unit of country A with rockets or by directly attacking with planes will lead to war with country B.
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