Why is Armstrong a suspect in Mrs Rogers death ?

Dr. Armstrong gave Mrs. Rogers something to help her sleep, which leaves some of the others believing he had something to do with her death.

"Last night. You said yourself you'd give her something to make her sleep."

"Oh, that, yes. A harmless sedative."

"What was it exactly?"

"I gave her a mild dose of trional. A perfectly harmless preparation."

Blore grew redder still. He said:

"Look here - not to mince matters - you didn't give her an overdose, did you?"