Hi there! ^^
No they're not written the same and there's a slight difference in the pronunciation...
In fact, the past form of the verb 'kiku' (to hear/to ask) is 'kiita' 聞いた(きいた) and it's the direct application of the past tense grammar rule for a verb of this "group".
Shikashi, the past form of the verb kuru (to come) is an exception to the rule of conjugation for a verb of that "group". That's why it's read 'kita' but it should have been something like 'kutta'.