Thanks a lot, Rusty.
And...
I haven't got any coins.
Neither have I.
Is it correct?

Another way to say también:

I saw the game yesterday.
So did I. (Me, too - Yo también)

I often say it that way. I've also heard 'Nor do I,' but the most common response is 'Me, neither.'

By the way, 'I haven't got any change' is a better-sounding, and more likely sentence. We don't use coins in the same sense you are. If someone asked specifically for coins, we would say, 'I haven't got any coins.' But, mostly, when this question is asked, we assume someone wants change (cambio/vuelto) and we use that noun instead of coins.

Me, neither, this simplifies the question, as you can use it in the place of neither do I, neither am I and neither have I. Great!

I suppose you can use the same structures with different persons. For example:

I'm not going and neither are you.

Is this right?

Or, even:

It's not my fault, and neither hers is.

Rusty is right, "Neither do I" is correct, but you are correct in this instance too. "Neither have I" works too(I think I say it that way sometimes), but it seems a little foreign to us. You may hear "neither have I" more frequently in Britain. Another way of saying "neither do I" is "I don't either"

Thanks a lot, Rusty. I was thinking of a magician on stage asking for some coins from the public. ;)

and not considering a new vocation as mendigo pidiendos monedas a los
turistas en la calle montera

Poli? Have you ever been to Madrid? What kind of places in Madrid have you visited?

I think this changes the direction of the thread a little. But David is taking a Mexican siesta.... No hay moros en la costa.

It's not my fault, nor is it hers. -or- It's not my fault, and neither is it hers. -or- It's not my fault, and it isn't hers either.