The Short Answer: In Right-to-Charge States, Usually No
If you live in a state with a right-to-charge law, your HOA generally cannot impose a blanket ban on EV charging stations. These statutes were written precisely because boards were denying reasonable requests, and they void or override HOA rules that prohibit or unreasonably restrict an owner from installing charging within their own space.
That does not mean the board is powerless. Right-to-charge laws let associations impose reasonable conditions: requiring professional installation, approving the equipment and location, mandating that the owner pay all costs including the electricity used, requiring the owner to maintain and insure the station, and, in some states, requiring a liability policy naming the association. The board can regulate the how; in these states it usually cannot deliver a flat no.
If you are in a state without a right-to-charge law, the balance shifts hard toward the association. Your leverage is the governing documents — the CC&Rs, bylaws, and rules — and whether the board is applying them consistently. The rest of this guide works for both situations, but knowing which one you are in tells you how much law is on your side before you ever walk into a meeting.