The school district "will" only say...

[Elemoi]

The Oxford Advanced Learner’s Dictionary says:
will
8 used for talking about habits: She’ll listen to music, alone in her room, for hours.

He would spend hours on the telephone.

If you put extra stress on the word will or would in this meaning, it shows that the habit annoys you: He will comb his hair at the table, even though he knows I don’t like it.


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The school district will only say that this is a personnel matter that's being looked into.
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Does will mean the same thing as will?

 

[susiedqq]

"will only say" is an expression that means the school district is limited in what it can say about this issue.

The district cannot comment about the situation.

 

[2006]

"The school district will only say........." means that no matter how many times it has been or will be asked about this matter, it will not say more than "This is a personnel matter...". So the "will" relates to the future also.

If you say 'The school district only said.........', that just refers to the past and maybe they said it only once.
If you say 'The school district only says.......', that again refers to the past and the present tense indicates they said it more than once.

The above two sentences don't (necessarily) relate to the future.

If the school district is limitted by someone or something in what it can say, you can say 'The school district can only say......'.