Maybe! Bohemond claimed they did, and Pope Gregory IX complained to the master of the Hospitallers about it (and the master of the Templars as well).

The Templars and Hospitallers often acted on their own without coordinating with Jerusalem or Antioch. The Hospitallers had their own castles and fortresses, especially Krak des Chevaliers, near Tripoli, and Margat, between Tripoli and Antioch. They were never able to conquer any Muslim territory on their own, but they could launch raids and collect tribute in the form of money or food. On one occasion, in 1267, the Assassins paid “1200 dinars and 100 measures of wheat and barley” in tribute. When the Mamluks captured Krak (in 1271) and Margat (in 1285), the Assassins participated in both sieges.

The event that the Pope was complaining about was part of a confusing series of events known as the “War of the Antiochene succession”. Basically, when Bohemond III of Antioch died in 1201, the principality was claimed by his younger son, Bohemond IV, who was also the Count of Tripoli; and his grandson, the infant Raymond-Roupen (his father was Bohemond III’s elder son, who had died before Raymond-Roupen was born, in 1197).

During the war, Bohemond IV’s eldest son, also named Raymond, was murdered by the Assassins in the cathedral of Tartus in 1213. The Templars and Hospitallers had also been involved in the war of succession, and it was actually the Templars who handed over Antioch to Raymond-Roupen in 1216, so apparently Bohemond IV believed they were involved in Raymond’s murder in 1213.

Eventually, Raymond-Roupen took Antioch in 1216, but Bohemond took it back in 1219. Bohemond IV died in 1233 and was succeeded by his second son, Bohemond V.

In 1236, Bohemond V complained to Gregory IX, that the Hospitallers and Templars were protecting the Assassins from their mutual enemies (the various local Muslim emirs in Aleppo, Homs, etc.) in return for tribute money. Nobody minded if the military orders forced the Assassins to pay tribute! But they shouldn’t be offering protection in return.

Pope Gregory acknowledged that the Assassins had murdered Bohemond V’s brother Raymond in 1213. He also noted that it was “insinuated” that the military orders may have been involved. But Gregory doesn’t directly say they were behind the murder, just that it was pretty suspicious that they were protecting the Assassins, and the Assassins had then murdered Raymond.

Sources:

Jonathan Riley-Smith, The Knights Hospitaller in the Levant, c. 1070-1309 (Palgrave Macmillan, 2012)

Judith Bronstein, The Hospitallers and the Holy Land: Financing the Latin East, 1187-1274 (Boydell, 2005)

Jochen Burgtorf, “The Antiochene war of succession”, in The Crusader World, ed. Adrian Boas (University of Wisconsin Press, 2016), pp. 196–211

Gregory's letter is in Latin, but if you want to read it, it's #3294-3295 in Lucien Auvray, Registres de Grégoire IX, vol. 2 (Paris, 1907)