Depreciation on real estate is only applicable when that real estate is utilized for the production of income. So if you are paying rent to the other TIC "AND" the recipient of that rent is reporting it as income on their tax return, then the recipient of that rent can depreciate the value of their portion of ownership that you are paying them rent for.
But typically, when you have a situation such as yours there is no formal rental contract involved and each TIC just pays their share of the expenses (mortgage, insurance, property taxes, etc.) So there's really nothing being rented per-se.
If you have two TICs and each has 50% ownership with only one of the TICs living in the property as their primary residence (or 2nd home for that matter), if each of you is paying one half of the expenses then there's no rental activity taking place. But if you are paying your half of the mortgage, property taxes and insurance, and then paying an additional amount to the non-resident TIC for the use of "their half" of the property, that additional amount "could" be considered rent which the recipient would report as income on their own tax return using SCH E.
