Does touching a dead body break wudu?

The body of a believer isn't impure

The Prophet ﷺ told Abu Hurayrah, "Subhan Allah! A believer never becomes impure" (Sahih al-Bukhari 283). Most scholars apply this to the dead as well: a Muslim's body stays pure after death, which is why it is washed out of honor and care, not to remove filth. Islam treats the human body with dignity in life and after it.

So if you hold your grandmother's hand in the hospital after she dies, or kiss your father's forehead, your wudu is still valid. The list of things that actually break wudu is short. See What breaks wudu?

Washing the body (ghusl al-mayyit)

Washing the deceased is a communal duty, usually done by a few family members or trained volunteers of the same sex. The Prophet ﷺ told the women who washed his daughter to wash her three or five times or more, with water and sidr leaves (Sahih al-Bukhari 1253), starting with the right side and the places of wudu.

A narration in Sunan Abi Dawud says that whoever washes the dead should take a bath. Scholars differ on how strong it is and what it means. The majority of the four schools say a bath afterwards is recommended (mustahabb), not obligatory, and the Hanbali school also recommends wudu for whoever carries the body. In practice, most people who wash a body simply shower afterwards, which covers every view. If you need a refresher, see How do I do ghusl?

Non-Muslim relatives

Touching the body of a non-Muslim relative doesn't break your wudu either. You can sit with them, hold their hand and grieve. Questions about their funeral are a separate matter. See Can I attend my non-Muslim grandma's funeral as a Muslim?

When you might need wudu again

Touching the body isn't the issue, but the ordinary things that break wudu still apply. If you use the bathroom while at the hospital or funeral home, or fall into a deep sleep, renew your wudu before you pray. If a body fluid like blood gets on your clothes, wash that spot before praying.