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1. I think he may not have noticed me.

When one wants to change 1 to the past tense, is it obligatory to change the tense of "may" into "might"?

2. I thought he might not have noticed me.

Or should "may" be preserved as such?

3. I thought he may not have noticed me.

Which is the sentence to choose?
Comments 
"Might" is the correct one.
For many people, both "may have" and "might have" are correct and used for the past. There's more doubt in "might have."

Things are a bit complicated and controversial. One of the points of view is here:

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http://www.orlapubs.com/AL/L39.html

potential MAY (HAVE)

used for possibilities in non-past time; may have is used for possibility in any past time up till now; e.g.
"They may (have) put it there."
One cannot say
"It may have survived"
when it is known that it didn't survive or hasn't survived!

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conditional-potential
MIGHT (HAVE) (past) past-posterior

used for doubtful possibilities in past time; e.g.
"They might have put it there yesterday";
"They said that it might arrive on time."

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Teleostomi1. I think he may not have noticed me.

When one wants to change 1 to the past tense, is it obligatory to change the tense of "may" into "might"?

2. I thought he might not have noticed me.

Or should "may" be preserved as such?

3. I thought he may not have noticed me.

Which is the sentence to choose?

"May (not) have" is just fine there.
Do you mean that after the verb "thought", which is used in past, it's fine to use "may"? I thought he may not have noticed me? But what about sequence of tenses? Or I don't get something? Emotion: tongue tied
"may" is a modal verb
as such, it's less related to tense than to mode/modality
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Thanks to all concerned for your help!

Marius, you inspired me! I have another question related to your post. I hope I'm not bothering you too much, but I'd be very happy if you would take a look at it.