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A permanent Level 2 installation adds value to the property, so many landlords are amenable, provided the work is done by a licensed electrician and a permit is pulled. Never do DIY electrical work on a rental property.
If you install a NEMA 14-50 outlet, the outlet stays with the house when you leave, but you can unplug your $600 charging station and take it to your next home. Just ensure the installation meets the new GFCI electrical codes.
In some states, "Right to Charge" laws mandate that landlords must allow tenants to install an EV charger at the tenant's expense, provided it meets safety codes and the tenant signs a liability agreement.