K-1 for Non-Resident State

I am a full-time resident of California, but have K-1 income and K-1 losses from a Limited Partnership in New York.  Do I need to file taxes in New York State as well as California and Federal?  If so, how do I tell California that I'm paying taxes on that income in New York (or, conversely, if I report as income on my California return, how do I tell New York that I paid taxes on it in New York)?

 

Also, if I DO have to file a New York return, how do I tell them that I paid state income tax for my non-K-1 income in California so they don't charge me taxes in New York for that income?

 

I'm using TurboTax Home and Business, but don't want to pay for 2 States if I can avoid it!