I am looking for the name of an old black and white movie, the year it
was made, and the name of the main character, a little blonde-haired
girl.  The plot is that the little girl lives with her mother in an
apt. bldg.  Her is father is away from home for some reason.  The
little girl steals a prize won by a male classmate of hers and then
causes the death of the little boy by drowning him.  She goes on to
cause the death of her neighbor, an old lady who has a pet bird.  She
tries to frame the building handyman and tries to burn his room using
stolen matches and packing material from a gift she had received (a
pair of skates, I think).  The murdered boy's mother plays a
significant part on this movie.  I recognize her, but don't know her
name.  She comes to the girls apartment several times wanting to know
more about the death of her son.  She's drunk and distraught.  The
little girl succeeds for a while in hiding her evil ways from her
mother, but in the end the little girl's mother finds the stolen prize
in the girl's bedroom and put the pieces together and knows how evil
her daugher is.  I last saw this old black and white movie on a cable
old movie channel in the late 1990s.  The movie ends with the little
girl being killed by a lightening strike.

The movie you're remembering is "The Bad Seed," starring Patty
McCormack as Rhoda Penmark, a sweet-looking little blonde girl who is
actually a cold-blooded murderess. Nancy Kelly played Rhoda's mother,
and Eileen Heckart had a memorable supporting role as the frantic
alcoholic mother of a young boy who was murdered by Rhoda because
Rhoda wanted a penmanship medal that the boy won. The black-and-white
version of "The Bad Seed" was released in 1956. There was a mediocre
made-for-TV color remake in 1985, but the original has not lost its
punch.

The script of "The Bad Seed" was adapted from a play, and the play was
adapted from a novel. In both the play and the novel, Rhoda survived,
presumably to continue her murderous ways. The movie's ending, in
which Rhoda is struck by lightning on the same pier where she had
drowned her classmate, was an attempt to make the film more morally
palatable to audiences and critics of the 1950s.

"Christine Penmark comes to believe that her young daughter Rhoda is
responsible for the death of Claude Daigle, a boy at school who won
the penmanship medal which Rhoda felt she deserved. Christine's
suspicions are magnified when she discovers the medal in Rhoda's
possession. Next the handyman Le Roy is ?accidentally' set on fire
after taunting Rhoda with accusations about the murder. Gradually
Christine becomes certain in the belief that she, an orphan, is the
daughter of a convicted murderess and has managed to transmit a
hereditary ?bad seed' to Rhoda...

The biggest sin the film conducts is its ending, which has Rhoda walk
out to a pier in search of the medal only to be crisped by a seemingly
divine lightning bolt - an appallingly tacky ending that was added to
yield to the righteous morality demanded by the Hays Code that
evildoers must be seen to be punished."

The SF, Horror and Fantasy Film Review: The Bad Seed
http://www.moria.co.nz/horror/badseed.htm

"This chiller about the 'perfect' Rhoda Penmark with her long blonde
braids and cold, cold heart stars most of the play's cast---Patty
McCormack as Rhoda, Nancy Kelly as her mother, Henry Jones as Leroy
the apartment handyman and Eileen Heckart as the mother of one of
Rhoda's schoolmates. While her pilot husband is away, Mrs.Penmark
begins to suspect there's something wrong with her perfect little
girl. You bet there is, she's a cold-blooded killer! As Rhoda's list
of victims grows, so does her mother's terror as she begins piecing
together the clues and facts. The film, shot in stark black & white,
appears stagy but this works fine because it's all about the
performances. They're brilliant."

Amazon.com: The Bad Seed
http://www.amazon.com/exec/obidos/tg/detail/-/B00027JYNK/104-5558882-9052756?v=glance

Google search strategy:

Google Web Search: "the bad seed" 1956
://www.google.com/search?hl=en&q=%22the+bad+seed%22+1956

I hope this is helpful. If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

That was exactly what I was looking for.  I knew the plot, but without
knowing the name of the movie or names of any characters it had been
impossible for me to find the answer.  Great job and thanks!!