That depends what you mean by "overdose". If you're asking how much Hyrdoxyzine (Vistaril; Atarax) is required to kill or seriously injure a person, the short answer is, quite a bit. Hydroxyzine is typically taken in 25mg - 50mg dosage units and it's not uncommon to see people taking 100mg Hydroxyzine if they're familiar/have a tolerance.
I don't have a lot of hard data regarding Hydroxyzine "abuse". We have a lot more information on the more common Diphenhydramine (Benadryl). Diphenhydramine also comes in these same dosage units. Most people will report symptoms of delirium/hallucinations beginning at ~300mg Diphenhydramine. With this in mind, I think it's safe to say that similar dosages of Hydroxyzine will produce these same symptoms. Note: these symptoms are often described as highly distressin both mentally/physically. Most people who go on an "antihistamine trip" regret the experience greatly.
Going higher with the dosages, you start to see very disturbing side effects that run the gamut:
Convulsions/Seizure
Gastrointestinal Disturbances (Vomiting; Diarrhea)
Organ Failure
Delirium/Hallucination
Tachycardia
People do die from antihistamine overdose. It is not a safe or advisable practice. Basically, you should only take antihistamines in dosages close to what the prescribed dosages are. Going with a higher dosage doesn't increase the desired effects of sedating antihistamines. As you go higher, the cost/benefit ratio gets extremely small.
If you're looking for a high or even a means of committing suicide, this is not the way to go.