NOT TRUE. Page Six reported on November 12, 2007: "Kate Hudson was in and out of her NYC apartment on Saturday in her fab gray coat. As her ex Owen Wilson has been making his mark on the Manhattan dating scene, apparently she's been having some fun of her own. Page Six reports that Kate was spotted making out with Heath Ledger at Beatrice Inn on Thursday night. Even though her rep is denying the rumors, what do you think about these two as a couple?"
"RTÉ.ie: Hudson denies Heath Ledger romance
Originally Published / Wednesday, 14 Nov 2007
Actress Kate Hudson has dismissed reports that she recently hooked up with Heath Ledger, branding the rumours "absolutely false."
The pair were allegedly spied enjoying a romantic night out last Thursday, at the famous Beatrice Inn in New York, where they were reportedly seen "kissing."
But Hudson’s rep insists the reports have been wildly exaggerated, telling PageSix: "This is absolutely untrue. They ran into each other and chatted briefly, but that was the extent of it.""
https://www.rte.ie/entertainment/2007/1114/411795-hudsonk/