I know that when a sentence begins with "I wonder" followed by a question, it is typically ended with a period.
I wonder why that is.
However, when "I wonder" is moved to the end of the sentence, does the same rule apply?
Why is that, I wonder?
It seems harder to deny the writer a question mark in this case if one is felt.
Both are correct English.
The first sentence has an embedded question object complement of a mental perception verb, and, as described here, sentences like these are often intoned as questions, because they're intended as requests for information. When a writer wishes their sentence to sound like a question in the mind's ear of the reader, they use a question mark; otherwise, not. This is very ordinary.
The second sentence has undergone a Dislocation, wherein the embedded question is moved to the front of the sentence, presenting a question form and signalling a bald request for information. And therefore, it is almost always punctuated with a question mark in writing; this is also very ordinary.
I wonder why that is. Is a question asked in a manner not expecting any answer in response. It is in it's own way telling the answer.
Whereas Why is that, I wonder? is asked to have a answer in response, that's why we use a question mark over here.
A quick survey of Google Books reveals that in both forms are commonly written with, and without a question mark.
Without a question mark, both forms become a statement of fact.
I wonder why that is.
Why is that, I wonder.
You can imagine them spoken with a downward inflection on the last syllable.
With a question mark, they are questions, perhaps rhetorical, but you can imagine them being spoken with an upward inflection, as if inviting an answer.
I wonder why that is?
Why is that, I wonder?
If you phrased your sentence,
I wonder, why is that?
it would require a question mark as well. The distinction is not where "I wonder" occurs, but the subject-verb inversion in "why is that"/"why that is". Subject-verb inversion is the grammatical way to form questions using the "wh" words which, why, how, who, what, and where. Grammatically, your first sentence is a statement.
The first one is more grammatically correct and you are right to mention that it does not need a question mark "I wonder why that is." 'I' is the subject and 'wonder' is the verb.
The second one is less grammatically correct and based more on colloquial speech patterns. In that regard, the question mark reflects the questioning tone that usually accompanies the spoken word (frequently this takes the form of going up in tone at the end."
