When not in school where does she normally reside?

Other than holidays and occasional weekends she doesn't go home per se.   She will be with her mother in Orlando about twice as much as her time with me.

Is IRS offering you the chance to show that she is your dependent ?

They are claiming that 2 people filed, so they are asking for me to demonstrate that she is my dependent or amend my return.  I am waiting to hear back from my daughter if she filed this year and claimed herself or if my ex wife claimed her.

It doesn't matter what they did if you can convince the IRS.

The letter indicated that "If you find you're entitled to claim the dependent or qualifying child, you do not need to write us or send any thing to us".   Based on this and your reply, I suppose I should leave it alone?

I find that sentence surprising. But, that just shows I'm no expert on the IRS's handling of these conflicts.

previously you said " they are asking for me to demonstrate that she is my dependent"

maybe they will ask for supporting evidence in a future letter.

@fanfare Thank you for your help.

@DoninGA Did you have additional clarifications you can suggest regarding my question?

From my understanding of the IRS procedures, when the same personal exemption is claimed on two or more tax returns the IRS will send a notice to all parties requesting the information that you received.  If neither party amends their tax returns to remove the personal exemption then the IRS will send another notice to require proof from each party that they were entitled to claim the exemption.
See this IRS 886-H-DEP  for the supporting documents that are required - <a rel="nofollow" target="_blank" href="https://www.eitc.irs.gov/eitc/files/downloads/f886-h-dep.pdf">https://www.eitc.irs.gov/eitc/files/do...>
The party that cannot prove they were entitled to the personal exemption must pay back any tax refund received based on that exemption plus penalties and interest.

@DoninGA That's perfect!   Thank you!

From your comment above "...Other than holidays and occasional weekends she doesn't go home per se.   She will be with her mother in Orlando about twice as much as her time with me..."

It would appear that your home would not be her home except for the "temporary absence" to attend school.   If that is the case then you probably do not meet the "lived with you more the half the year" test to be your Qualifying child.   

However, she might not meet that test for the other parent either depending on the exact cercumstances, so she might not be the Qualifying Child dependent of either parent, but could possibly meet the Qualifying Relative test for one parent, if that parent provided more than half of her total support for the year and her taxable gross income was less than $4,050. Who could claim would then come down to why provided the support since living with you is not a Requirement for a Qualifying Relative.

---Tests to be a Qualifying Relative (& Unrelated Persons)---

       (Must meet ALL of these tests to be a dependent)

1.  The person cannot be your qualifying child or the qualifying child of any other taxpayer.

2. The person either must be related to you, or must live with you all year (all 365 days - There are exceptions for temporary absences such as school, illness, business, vacation, military service) as a member of your household.

3. The person's gross income for the year must be less than $4,050 (tax-exempt income, such as certain social security benefits, is not included in gross income)

4. You must provide more than half of the person's total support** for the year.

5. The person is not filing a joint return.

In any case, the person must be a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico

The above is simplified; see IRS Publication 17, for full information.
<a rel="nofollow" target="_blank" href="https://www.irs.gov/publications/p17/ch03.html#en_US_2016_publink1000170933">https://www.irs.gov/pub...>

** Worksheet for determining support
<a rel="nofollow" target="_blank" href="https://www.irs.gov/publications/p17/ch03.html#en_US_2016_publink1000171012">https://www.irs.gov/pub...>