I’m reminded of the old joke:

'avwI'vaD jatlh qama' «jIghung»

   jang 'avwI' «jIghung je»

jatlh qama' «jI'oj»

   jang 'avwI' «jI'oj je»

jatlh qama' «jIDoy'qu'»

  jatlh 'avwI' «jIDoy'be'!» 

A prisoner says to the guard, "I am hungry."

  The guard replies, "I am also hungry."

The prisoner says, "I am thirsty."

  The guard replies, "I am also thirsty."

The prisoner says, "I am very tired."

  The guard says, "I am not tired!"  [PK]

To help learners understand the grammar, Okrand’s translation was literal and somewhat formal.  There’s no reason you couldn’t render the guard’s replies more colloquially as “Me too” or “I am too” and “Not me!” or “I’m not!”  (We’ve seen other instances where Klingon sometimes repeats a verb or noun where an English speaker would omit them.)

Voragh

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From: SuStel

In my opinion, the Klingon equivalent to me too is to repeat the verb in

the first person and add a je. For example:

Klingon 1: romuluSnganpu' vImuS! I hate Romulans!
Klingon 2: vImuS je! Me too!

Klingon 1: SIbI' ruchbe'chugh chaH, jImej. If they don't get on with
 it right now, I'm leaving.
Klingon 2: jImej je! Me too!