If I have expenses for my rental property in the month of January 2015, can I claim these on my 2014 taxes?

in general no; you cannot deduct expenses from a present year on previous year’s tax return. You can only deduct expenses in the year that you paid them.

Each return deals with its own year.You can’t just lump deductions or income or anything else from a previous(prresent) year in with this year’s (prev)tax information.

One of the exceptions to this rule is the tuition and fees deduction, which allows you to claim qualified education expenses from the previous year as long as they were for school sessions that began in January-March of the tax year you are currently filing for.