You must file a tax return in the U.S., there are benefits due to the double taxation treaty that exists between Ireland and the U.S. so you will not pay twice.
In my case I pay my Accounant closer to $1000 rather than $450 but I have a few properties, the tax paid is minimal, there is so much that can validly be deducted.
It is my understanding that if no income taxes are paid that 10% of the price achieved at disposal is held back for the IRS, I got that information from my Accountant.
KKelliher lists many items in his post, as the O.P. already owns U.S. property they will be familiar with the overhead costs of which from my point of view as an investor are as follows.
*Payment of property taxes
*Payment of Association monthly fees
*Accountant charges - deductable.
*Landlord Insurance - about $160 annually
*Management charges and usually one months leasing commissions
And it is still worth doing.