The short answer is that a school district can use a private evaluation. More often than not, they will still want or need to do their own evaluation.
School district evaluations are suppose to be multidisciplinary evaluations. An Occupational Therapist (OT) evaluation alone would not meet that criteria , but there are no absolutes with-sds. A private neuropsychologist evaluation or multidisciplinary evaluation might, but the sd can still elect to do their own evaluation. In these instances, the sd must "consider" the private evaluations if the report(s) are given to the sd.
In part, sd evaluations criteria consists of:
http://idea.ed.gov/explore/view/p/%2Croot%2Cstatute%2CI%2CB%2C614%2Cb%2C
Statute: TITLE I / B / 614 / b
(b) Evaluation Procedures.--
(1) Notice.--The local educational agency shall provide notice to the parents of a child with a disability, in accordance with subsections (b)(3), (b)(4), and (c) of section 615, that describes any evaluation procedures such agency proposes to conduct.
(2) Conduct of evaluation.--In conducting the evaluation, the local educational agency shall--
(A) use a variety of assessment tools and strategies to gather relevant functional, developmental, and academic information, including information provided by the parent, that may assist in determining--
(i) whether the child is a child with a disability; and
(ii) the content of the child's individualized education program, including information related to enabling the child to be involved in and progress in the general education curriculum, or, for preschool children, to participate in appropriate activities;
(B) not use any single measure or assessment as the sole criterion for determining whether a child is a child with a disability or determining an appropriate educational program for the child; and
(C) use technically sound instruments that may assess the relative contribution of cognitive and behavioral factors, in addition to physical or developmental factors.
(3) Additional requirements.--Each local educational agency shall ensure that--
(A) assessments and other evaluation materials used to assess a child under this section--
(i) are selected and administered so as not to be discriminatory on a racial or cultural basis;
(ii) are provided and administered in the language and form most likely to yield accurate information on what the child knows and can do academically, developmentally, and functionally, unless it is not feasible to so provide or administer;
(iii) are used for purposes for which the assessments or measures are valid and reliable;
(iv) are administered by trained and knowledgeable personnel; and
(v) are administered in accordance with any instructions provided by the producer of such assessments;
(B) the child is assessed in all areas of suspected disability;
(C) assessment tools and strategies that provide relevant information that directly assists persons in determining the educational needs of the child are provided; and ....
You'd still need to refer your child in writing and via Certified Mail.