Purity: Conditions for the Person Performing Salat al‑Mayyit
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 585:
It is not necessary for someone who wants to perform salat al‑mayyit to have wuḍūʾ, ghusl, or tayammum, or for his body and clothes to be pure. In fact, even if his clothes are usurped there is no problem, although it is better that he observe all the rules that apply to other prayers. One must refrain from doing anything that breaks the form of salat al‑mayyit, and based on obligatory precaution, one must abstain from talking, laughing, and turning their back to the qibla.
-Ayatullah Sistani, Practical Laws of Islam, Purification (Taharah)