It’s unclear - it may have been random.
Why exactly the Dark Lord sent Narcissa, rather than anyone else, to check if Harry was alive is never made clear. All that’s seen about his method of choosing is that he hits someone with a spell and orders them to verify if Harry is truly dead.
“You,’ said Voldemort, and there was a bang and a small shriek of pain. ‘Examine him. Tell me whether he is dead.’
Harry did not know who had been sent to verify. He could only lie there, with his heart thumping traitorously, and wait to be examined, but at the same time noting, small comfort though it was, that Voldemort was wary of approaching him, that Voldemort suspected that all had not gone to plan …”
- Harry Potter and the Deathly Hallows, Chapter 36 (The Flaw in the Plan)
It isn’t made clear if the Dark Lord actually aimed his spell at Narcissa, or if he was using it as a way of random selection. If he did aim his spell intentionally at Narcissa, it’s still not clear what his thought process was behind choosing her. There’s no obvious reason why he’d choose her over everyone else, nor are his thoughts behind any choice explained in the text - it’s not even clear he made one. If the spell was a method of randomly selecting who would verify Harry’s death, then the answer is simple - his spell happened to hit Narcissa, deciding she’d be the one to check if Harry was dead.