Mr. Hyde has the key to Jekyll's home because Jekyll provided it for him.
"I saw Mr. Hyde go in by the old dissecting-room door, Poole," he said. "Is that right, when Dr. Jekyll is from home?"
"Quite right, Mr. Utterson, sir," replied the servant. "Mr. Hyde has a key."
"Your master seems to repose a great deal of trust in that young man, Poole," resumed the other musingly.
"Yes, sir, he do indeed," said Poole. "We have all orders to obey him."
Dr. Jekyll and Mr. Hyde