You mention you are in an apartment. Do you have the approval from the landlord to install an air conditioner? Will it become his property once you install it?
Well...how it works here, after you move out, you remove the A/C and just need to "tapar el hueco"
You would have to read the lease agreement. It may have a clause that states that any improvements done that are attached to the property remain.
Well, at the time of your move-out you just "dis-attach" it, so where's the "improvement"?... ehh.. mira, aqui nunca habia un aire, yo hice ese hueco para cojer mas fresco.... pero yo le tape, cual es tu problema?
Anyway, most people here "live" the last two deposits (even the landlords suggest to do that, I have heard it with my own ears), so... anyway, there's nothing to haggle about.
Anyway, "improvements" as mentioned in lease contracts (yes there are many lease contracts with that, residential and commercial) are to the respect of INMUEBLE (real estate, construction, etc.) not to MUEBLES y ELECTRODOMESTICOS. As classified by DGII, A/C is electrodomestico, so .... the landlord would actually have no legal recourse.
On the other hand, I have seen many contract clauses unenforceable in the DR. Example: my friend bought a land in barahona, and put some contract clauses in the contract with the seller, but the lawyer (GuzmanAriza) warned him those clauses would be virtually unenforceable in the DR. They would be enforceable anywhere else in the first world... so there you have it.