NEITHER NOR
EITHER OR

the FORMAL way to use neither is... neither can i, neither do i or nor do i...

you use EITHER when a negative clause is implied.. for example i do NOT want to go to school EITHER.

NEITHER CANT be used when a negative clause is implied... for example, you CANT say: i do NOT want to go to school NEITHER.. that's wrong! the correct way to say it..NEITHER DO I, NOR DO I.

now it is common to use ME NEITHER or ME EITHER(they are BOTH informal like dont/do not and doesnt/does not) it is NOT just me neither*.. but still it is more acceptable to say me NEITHER as a short answer than me EITHER..

even though they are both used, EITHER was NOT meant to be used that way as me either ..just becuz people get lazy and just rather say me either(normal in american english) EITHER's correct use is to use it with sentences with negative clauses on it (dont, doesnt, isnt, im not, arent) NEITHER CANT be included in this cuz that would mean you are using double negation which is WRONG

but for the original question ... THEY both are informal but *me NEITHER* is still correct.. some people use me EITHER and even though people understand it and it's normal in american english to say it..GRAMMATICALLY correct the use of either is not for me either