For single member LLC - you do not file any tax return and your business activity is treated the same way as it is a solo proprietorship. In this case the business will have the same tax year as the member.
If LLC has several members - that is in general a partnership and partnership income tax return is required.
Form 2553 Election by a Small Business Corporation - http://www.irs.gov/pub/irs-pdf/f2553.pdf is used if you want to treat your LLC as S-corporation fro tax purposes.
The same form is used if you want to select different tax year for your business.
See instructions for details - http://www.irs.gov/pub/irs-pdf/i2553.pdf
Let me know if any clarification is needed.
As a partnership - you would file firm 1065 - http://www.irs.gov/pub/irs-pdf/f1065.pdf
Please see requirements for determination of Accounting Periods on the page 5 instructions - http://www.irs.gov/pub/irs-pdf/i1065.pdf
A partnership is generally required to have one of the following tax years. Note. In determining the tax year of a partnership under 1, 2, or 3 above, the tax years of certain tax-exempt and foreign partners are disregarded. See Regulations section 1.706-1(b) for more details. The tax year of a majority of its partners (majority tax year).If there is no majority tax year, then the tax year common to all of the partnership's principal partners (partners with an interest of 5% or more in the partnership profits or capital). If there is neither a majority tax year nor a tax year common to all principal partners, then the tax year that results in the least aggregate deferral of income. Some other tax year, if: -- The partnership can establish that there is a business purpose for the tax year;-- The partnership elects under section 444 to have a tax year other than a required tax year by filing Form 8716, Election to Have a Tax Year Other Than a Required Tax Year. -- For a partnership to have this election in effect, it must make the payments required by section 7519 and file Form 8752, Required Payment or Refund Under Section 7519. A section 444 election ends if a partnership changes its accounting period to its required tax year or some other permitted year or it is penalized for willfully failing to comply with the requirements of section 7519. If the termination results in a short tax year, type or legibly print at the top of the first page of Form 1065 for the short tax year, “SECTION 444 ELECTION TERMINATED”; or The partnership elects to use a 52-53 week tax year that ends with reference to either its required tax year or a tax year elected under section 444. Change of tax year. To change its tax year or to adopt or retain a tax year other than its required tax year, the partnership must file Form 1128, Application To Adopt, Change, or Retain a Tax Year, unless the partnership is making an election under section 444.
If you use form 8716 - http://www.irs.gov/pub/irs-pdf/f8716.pdf for Election To Have a Tax Year Other Than a Required Tax Year - it must be signed and filed by the earlier of:
1. The 15th day of the 5th month following the month that includes the 1st day of the tax year the election will be effective or
2. The due date (not including extensions) of the income tax return for the tax year resulting from the section 444 election.
see for reference instructions for that form - scroll down.