Did Nikola Tesla invent an electric car?
I’ll begin by agreeing with what some of the other people have said who have already answered ahead of me: he did not invent the electric car but there are stories of him making improvements and those improvements never reached commercial outlets which is not surprising because after 1903 he was not commercially successful with anything not for lack of trying but probably because he was already too famous already and you know what happens when somebody gets very famous as opposed to just a little famous a lot of jealousy can crop up and act as a resistance, an unnatural hedge, against the inventor making any further progress in the commercial sector with his ideas, because he’s no longer popular!
To understand those improvements, if they be true, would require the capacity to understand how the potentialities of capacitance, inductance, frequency, and phase shift, can be used as methodologies for boosting energy to such a degree of amplification that the residual energy in our environment would be sufficient to power a car and not just any old car but a race car at that.
In fact, that is what Tesla motors has based their car off of: an electric race car who’s motor controller was invented by Alan Cocconi who contributed his motor controller to the General Motors EV-1 and he is interviewed in the movie called “who killed the electric car” and he founded a company called AC propulsion for manufacturing that specialty race car running on electricity because that was his hobby was to race cars so long as they were powered by electricity!
So, it is possible that Tesla motors was not the first to popularize the conversion of a race car into a consumer product.
But most people do not possess the skill of understanding to appreciate what I have just described which is an understatement. Because they can’t imagine how additional energy can come out of capacitance, inductance, frequency and phase shift at a factor of gain that would dwarf the initial energy which tickled these four factors into a state of overly responding with more energy than could possibly be consumed! 
They lack the skill because they are hampered by their belief in the conservation of energy commands everything. Well, that’s not the way I see it.  Conservation of energy has a very restricted domain. Outside of that domain, it cannot go.
There are free oscillations which transcend the conservation of energy, but forced oscillations cannot! Also, forced oscillations can exist without free oscillations but free oscillations cannot exist without forced oscillations. So, in an indirect manner, conservation of energy is the basis of everything and is also indirectly at the basis of overunity! But conservation of energy is directly restricted to forced oscillations since it cannot address why free oscillations can evolve energy from electrical reactance on top of whatever conserved energy exists within forced oscillations.
Forced oscillations make free oscillation possible. Conservation of Energy makes Overunity possible.
Free oscillations are dependent upon forced oscillations for its very existence on the one hand, but free oscillations are not constrained by forced oscillations or else they would not be free to oscillate.
In other words, …
Free oscillations are not forced oscillations. Free oscillations are free to oscillate based on reactant criteria which forced oscillations do not have access to. Forced oscillations merely rely upon Ohm’s Law and Kirchhoff’s laws while ignoring electrical reactance.
Oscillations are a mixture of the two. So, consequently, conservation and non-conservation coexist in a state of mixture in any electrical situation to one degree of proportional ratio versus the other.