Allowable depreciation on income property, whether used ( recognized ) or not still reduces your basis and becomes important when you sell the property. Additionally because this is a gift it opens up two items--> (a) your basis of property gifted to you is the same as that of the donor --- thus while the depreciation may not be large ( assuming that the donor had held the property for a longtime and that the property inflation is reasonable ), the effect on the adjusted basis is till real. ; (b) if the gift is from a foreign person and to you when you had become a citizen/ resident of USA, you may have to report the transaction -- no tax consequence.
Please , when you say gifted, I hope you do not mean left to you as a part of inheritence, because in that case the basis is the Fair Market Value of the property at the time of death of the decedent.
If you have not been recognizing the depreciation of income property , then Ideally you should amend the returns of the past years --- the only issue sometimes is that , if this results in a refund ( due to amendment ) , IRS will reocgnize but may not give you the refund for returns that are more than 3 years old.
To recognize depreciation, you have to enter all the details on the asset worksheet ( tell TurboTax that you have a foreign real-estate -- the basis, the year you started renting out etc. ( also land value ) etc. etc. . Turbo will than do the rest and provide you with a depreciation schedule. Use this to amend the past returns.
Hope this helps and if you need more help, please add your questions as part of comments
Thank you for your answer! Follow up questions: is depreciation mandatory? Can I just not take it?
there is no requirement to "take" it but whether you do or not, it still counts as a reduction to your basis in the property and thus increases your capital gain when you sell the property ( assuming the prices go up, in dollar terms ). Also note that by taking the depreciation, and if you end up with a loss on schedule-E, under certain conditions, that loss reduces your ordinary income and therefore your current tax liabilities