As you have asked about the exam pattern and syllabus of the Tamil Nadu Public Service Commission (TNPSC) Block Health Statistician (BHS) exam, I am giving you information about it, check below for the details

The TNPSC BHS Exam consists of the following features:

The exam is of Objective type i.e it consists of Multiple Choice Questions.
The exam consists of 2 Papers.
Paper I has 200 Questions & is conducted for 300 Marks.
Paper II has 100 Questions & is conducted for 200 Marks.
Duration of Paper I is 3 Hours.
Duration of Paper II is 2 Hours.
The exam will be set in both English & Tamil.
Paper I consist of Questions from any one of the subjects among Statistics/Mathematics as chosen at the time of applying.
Paper II consist of Questions from General Studies.

The TNPSC BHS Exam consists of the following subjects:

General Studies
Mathematics
Statistics

BHS Syllabus for General Studies

General Science.
Physics
Chemistry
Botany
Zoology
Current Events
History
Political Science
Geography
Economics
History and Culture of India
Indian Polity
Indian Economy
Indian National Movement
Mental Ability
Quantitative Aptitude etc

TNPSC BHS Syllabus for Statistics

Graphical Representation
Statistics
Probability
Binomial
Poisson
Geometric & Hypergeometric
Continuous Distributions
Curve Fitting
Linear and Quadratic Equation
Population and sample
Parameter and Statistic
Sampling Distributions
Estimation
Blackwell Theorem
Chi-Square Test
Tests of Hypothesis
Simple Random Sample
Analysis of Variance
Concept of SQC
Time Series
Trend and Seasonal Variations
Index Numbers
Linear Programming Problems
Basic Programming etc

TNPSC BHS Syllabus for Mathematics

Basic Mathematics
Analytical Geometry
Calculus
Statics
Real Analysis
Operations Research & Linear Programming
Algebra
Differential Geometry
Differential Equations
Dynamics
Statistics