OK, this was a film in color that I saw on TV as a kid.  It had a
young, female, blond star (I'm thinking Carol something..Lindley,
Cane, Lombard??). She had short pixie-like hair.  The timeframe of the
film was maybe 1965-1970.

The opening scene shows her pulling into the garage of a beach house
in a 1965ish red Ford convertible.  She obviously lives alone and is
wealthy. She goes for a swim in the ocean.  She emerges from the water
walking back up to the house while carrying (I'm not kidding) a
harpoon dart gun thing.  She sees a small child playing with a
beachball on her "private" beach and shoots it (the ball) with the
harpoon gun.
 
The storyline is a Dial M for Murder type remake.  She is seeing a
psychiatrist in the city who wants to have her committed for being a
little "off."  She somehow has an affair with a married professional
golfer on tour and
convinces him to kill the psychiatrist if she kills his wife in
exchange.
  
I'm pretty sure she kills the wife and he can't go through with his
end of the bargain.  He thought that they were only speaking about
the plan as a scenario and they were not really going to commit
murder.  In desperation, she kills the shrink also.  The rest of the
story is a little fuzzy, but I know in the end she frames him for the
murders and gets away with it.

Thanks in advance.

You are remembering "Once You Kiss a Stranger," starring Carol Lynley.

Here's a rather irreverent synopsis:

"Daft remake of STRANGERS ON A TRAIN with glacial Carol Lynley doing a
distaff femme fatale take on Robert Walker's classic role. She's
disturbed doll-faced Diana, who desires the death of her shrink, who
alone realises her malign potential and seeks to have her committed.
Fixating on perpetual golf pro runner-up Jerry (stone-faced Paul
Burke), she beds the hapless sap and manages to get the admittedly
soused sportsman to spout some incriminating pillow talk whilst being
unknowingly filmed and recorded by a hidden camera which thereby
appears to frame him for his superior golfing rival's subsequent
murder as he unwittingly plays into her hands during her switcheroo
murder plan pitch. Having held up her end of the bargain (and having
purloined both the murder weapon and, as per the original film, a
potentially incriminating cigarette lighter which is never flagged up
as the classic 'McGuffin' it was in the Hitchcock original, and which
both threaten to lead the forces of law and order to his door), the
murderous minx now expects him to follow through with his end of the
deal..."

Internet Movie Database: Once You Kiss a Stranger
http://www.imdb.com/title/tt0064760/

I recognized the movie instantly from your description. It's not a
very good movie by most standards, but I'm a big Carol Lynley fan from
way back, so I enjoyed it.

If anything is unclear, or if this is not the correct movie, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

Excellent!  I haved looked for this answer for years.

Thank you very much for the five stars and the tip! I'm always glad to
be able to help someone identify an old movie. I know how frustrating
it can be to have something like this stuck in your head for years on
end.

If you liked "Once You Kiss a Stranger," you might want to check out
"Strangers on a Train" and "Throw Momma From the Train," both of which
have a similar theme. Another movie that is a bit similar to "Once You
Kiss a Stranger" is "Pretty Poison," starring Tuesday Weld as a
psychotic, manipulative blonde who convinces the hapless Anthony
Perkins to collaborate with her in a murder plot.

~pinkfreud