Based on the short story "The Dead Man" by Ray Bradbury. The story was first published in Weird Tales (July 1945).

Miss Weldon: Drowning's a terrible thing.
Odd Martin: I know. I've been drowned.

Boy: Sometimes I see you walk by my house, not going anyplace.
Odd Martin: No place to go. I try thinking some place to go. Hard to think. Sometimes I almost know where to go. Then I forget. Once I thought go to a doctor, have him declare me once and for all dead. But somehow I never got there.
Boy: If you want, I'll take you.
Odd Martin: No, I'm tired but I'll wait. I'm curious to see what happens next. But I know I'm dead. Late nights I lay listening in my room, but no heartbeat in my ears, nor in my chest, nor in my wrists. Nothing in me but heart and mind. Maybe I'm still walking because I died young. Only 28 and not married. Always wanted to marry, never did. But sometimes there's something makes me stir. I think it's the wind. It brings all these great perfumes. Or the sight of a lady's just now curled hair, and or the sight of her tiny shoes on the sidewalk.

Changes from the short story:

* The sequence of Mrs. Weldon arriving in town isn't found in the story.
* In the short story, Charlie watches from his window and sees Mrs. Weldon and Odd enter the cemetery. In the episode, he accompanies them there and pronounces them man and wife to make it "official."