A neutral cleric will need to decide between good and evil. But I think that choice only determines whether they channel negative or positive energy and if they can spontaneously cast cure or inflict spells.
"A cleric can't cast spells of an alignment opposed to her own or her deity's (if she has one). Spells associated with particular
alignments are indicated by the chaotic, evil, good, and lawful descriptors in their spell descriptions."
Just wondering if a neutral cleric that worships a neutral deity just pretty much ignores this rule.
A neutral cleric whose deity is neutral can cast both good and evil spells.
As Some Random Dood mentioned, this cleric has the choice whether to spontaneously cast cure spells and channel positive energy, or spontaneously cast inflict spells and channel negative energy (but none of these four acts is in itself good or evil and any cleric can use cure or inflict as prepared spells).