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The fact that a rental property has been purchased via a 1031 - has no affect on reporting rental income.
If there are three joint tenants - those who actually receive rental income should claim it along with rental expenses.
If only one tenant receives rental income - he/she should be only one who claims it on the individual tax return.
If rental income is splitted between tenants - it should be claimed by each tenant.
In this case - tenants are acting as partners - and partnership tax return would be required - use the form 1065 - http://www.irs.gov/pub/irs-pdf/f1065.pdf
Income for each partner (pro-rated according to the agreement between partners - not necessary in equal amounts) should be reported on the schedule K-1 - http://www.irs.gov/pub/irs-pdf/f1065sk1.pdf
Rental income should be reported in the box 2.
Let me know if you need any help.
Taxable income is determined by the federal law - Title 26 - http://www4.law.cornell.edu/uscode/html/uscode26/usc_sup_01_26.html
Arizona tax laws for income tax is based on the federal tax law with some adjustments - http://www.revenue.state.az.us/FAQS/movingfaqs.htm
As you see on Arizona tax return - line 12 - the amount is taking from Federal adjusted gross income (from your federal return) - http://www.revenue.state.az.us/Forms/2008/individual/140.pdf
Additionals and subtractions based on Arizona specifics are reported on lined 13 and 15. There is no different treatment for partnership income reported on the schedule K-1.
So - in your situation - there is no difference between federal and Arizona income tax laws.
Arizona has different laws in some tax areas - for instance for property and sales taxes.